Recent advances in nano-opto-electro-mechanical systems

1 Introduction

Photons, electrons (holes), and phonons are several basic (quasi) particles in the field of physics. With the development of micro-/nano-technology and quantum information technology [1, 2] in recent years, people can already manipulate photons [3, 4], electrons (holes) [5, 6], and even phonons at the single-quanta level [7, 8]. During the several past decades, micro-/nano-technology has also promoted the rapid development of the micro-electro-mechanical systems (MEMS) field, where the interaction between mechanical and electrical degrees of freedom is widely studied. With the continuous reduction of device size, the MEMS field is gradually developing into the nano-electro-mechanical systems (NEMS) regime. When the size of the device is reduced to match the wavelength of light, a number of new types of micronano structures have emerged to combine with the field of nanophotonics. By studying the interaction of optical, electrical, and mechanical degrees of freedom, various applications of nano-opto- electro-mechanical systems (NOEMS) are explored, such as the control of photons, charges, and phonons, information processing at classical or quantum levels.

Tunable photonic devices have shown great application prospects and have gained more attention in recent years. A great deal of studies has been carried out to develop methods to realize such tunable photonics. The tuning principle mainly includes: Thermo-optic effect [9], electro-optic [10, 11] effect, and common optomechanical interaction in recent years. Each of these tuning mechanisms has advantages and disadvantages. There is an appropriate tuning range by temperature changes to tune photons, but the energy consumption is too high. The operation speed is getting faster, while the tuning range becomes smaller because of slightly changes of the light index with the modulation voltage [12]. Although the current electro-optic method is more mature, it still dominates the field of tunable photonics. But it does not have the ability to completely reconfigure the photonic structure or significantly change the coupling strength. The novel mechanical method is believed to be able to compensate for these defects and further accelerate the development of photonic technology [13].

The role of mechanical displacement has received increased attention across a number of disciplines. It is known to all that the electric drive of moving parts in optical cavities or waveguides can be used to adjust the phase or frequency of the corresponding light field to generate an effective electro-optic interaction. This interaction is bidirectional. The force exerted by light, such as the radiation pressure generated by light beam reflected by the mirror, may cause mechanical displacement of the object. In reverse, the displacement can produce voltage and current in a piezoelectric material or a capacitive sensor. In the past decade, the complex dynamics resulting from this coupling have been intensively studied in the field of optomechanics. Previous researches are focused on a single degree of freedom as electromagnetic fields, optical, or mechanical modes, while recent experimental advances have brought about the potential of hybrid systems [14]. The combination of optical, electronic, and mechanical functions opens up new applications, from the electrical tunability of optical and mechanical devices to the bidirectional conversion of microwave and optical quantum signals.

Compared with the current common tuning system, mechanically moving or deforming the structure has more advantages. Therefore in recent years, there have been more and more researches on the modulation of photons based on MEMS/NEMS. With the development of micro-/nano-manufacturing technology, since the 1960s, the scale of MEMS devices has become smaller and smaller, and the performance has also been greatly improved up to the nanometer size. Thanks to its easier-to-master chip integration and manufacturing process, the current NEMS equipment has been widely used in various fields. In this article, we will develop tunable photonic devices more comprehensively, and explore the excellent characteristics.

Here, we review recent developments in this emerging field of the hybrid NOEMS shown in Figure 1, by focusing on the fundamentals of the hybrid system and applications from various perspectives. We start with the discussion of the nanoparticles application. Furthermore, differences between NOEMS applications in classical information transduction and quantum information processing are also to be discussed in detail. More and more applications in particular for switching, routing and sensing in hybrid systems therefore offer a promising future to engineer and enhance the development of the NOEMS in the quantum regime.

Figure 1:

The latest application of the NOEMS. Applications to manipulate nanoparticles are mainly divided into charge control [15], photon control [16] and phonon control [17]. Applications to information transduction are divided into classical optical switches [18], sensors [19], and transductors [20]. Applications in the field of quantum are nanobeam photonic molecule [21], double-membrane photonic crystal cavity [22], and beam splitter [23].

2 Concepts of NOEMS

The mechanical properties of nano structures are different from micro ones. It has been found in experiments that mechanical properties are changed as the size of the structures decreases in various materials such as metal materials, composite materials, polymer materials, and semiconductor materials. Compared with MEMS, NEMS are highly sensitive to small mass, displacements, and forces. In 2003, Ono et al. [24] developed a nanocatilever hydrogen sensor with a resolution better than 5 × 10⁻¹⁸ g. And in 2005, Yang et al. [25] proved that a nanocatilever electromechanical device with a mass around 10⁻¹⁸ g could be used as a sensor to detect the mass of a DNA molecule bound to it [26]. In 2019, Schliesser et al. [27] used strong quantum correlation in a supercoherent optomechanical system to demonstrate the off-resonant force and displacement sensitivity, which reached 1.5 dB below standard quantum limit. This is a critical step in mechanical quantum sensing and further opens up the prospect of force sensing applications, which has brought many novel applications such as scanning force microscopes based on ultrasensitive silicon nitride (SiN) thin film sensors [28].

From the perspective of microscopic particles, the physical mechanism of NOEMS is essentially the interaction between photons, electrons, and phonons. The electro-optic effect between electrons and photons is enhanced by the control of phonons. The refractive index of a NOEMS device could be changed under an applied electric field due to the photoelastic effect caused by the inverse piezoelectric effect of the atomic lattices, which leads to an enhanced electro-optic effect. The diagram of the physical mechanism is shown in Figure 2.

Figure 2:

Interaction mechanism of nano-opto-electro-mechanical systems.

The first part of the electromechanical system is the conversion between charges and phonons. We generally discuss phonons in resonant lattices or in macroscopic parallel metal-like settings. The mechanical motion changes the energy U stored in the electrostatic field. And this changes the charge on the plate. Conversely, when the energy of a parallel capacitor plate changes, a force F = −dU/dx is generated. For electro-mechanical capacitors with metal plates, U = 1/2QV (Q and V are the charges on the plates and the voltage between the plates), the force can be written as F_e = 1/2V²dC/dx, where C(x) is the capacitance subject to displacement.

In the nanoscale optomechanical system, the essence is the conversion between photon and phonon. Under the adiabatic limit, the energy exchange of the electromagnetic system is faster than the energy exchange at the frequency of mechanical motion, so the electromagnetic system can be regarded as a resonator affected by mechanical motion. This ensures that U/ω (corresponding to the number of photons N_p) is constant, where ω is the optical frequency and the force can be written as F_p = −N_pℏdω/dx. This general expression links the optical force to the optomechanical coupling factor dω/dx, which can be derived from the solution of Maxwell’s equations. In the case of optomechanical (under the adiabatic limit) forces, the force can be written as |F| = U/L^eff, where the effective coupling length is Leff=|1ωdωx|−1. Under the control of optical and electrostatic forces, the mechanical deformation of the nanophotonic waveguide can be designed to provide a very strong and effective electro optical interaction in various materials including silicon.

3 Applications to photon, charge, and phonon manipulation

Over the last few decades, people have been able to manipulate single quantum in different ways. And carrier of single quantum can be single photon, charge, and phonon. The three types of nanoparticles defined from a quantum perspective constitute a hybrid NOEMS system from a macroscopic perspective, corresponding to the three aspects of optics, electronics, and mechanics, respectively. On the contrary, with the rapid development of quantum technology in recent years, NOEMS has gradually realized the control of nanoparticles. Next, we will take the excellent achievements of recent years as examples to analyze the application of NOEMS from the perspective of nanoparticles.

In recent years, more and more excellent achievements have emerged in the field of quantum that manipulate a single photon through electrical or mechanical means. In particular, many studies have manipulated single photon in reconfigurable integrated circuits to enable quantum photon networks. There are many interesting applications in this field, such as filters, beam splitters, and routers. With the rapid development of quantum communication, quantum calculation and high-precision detection, quantum light source plays an increasingly important role in the researches of quantum information technologies. The acquisition of single photon has gradually become one of the research topics at home and abroad. The ideal single-photon source emits only one photon in each excitation pulse, which is a kind of photon antibunching phenomenon. The ideal single-photon source needs to meet the following conditions: (1) Emitting a single photon at any time, so that the probability of emiting a single photon is 1; (2) once the photons are emitted, the efficiency of each photon in the ideal quantum channel is uniform; and (3) each photon emitted should be indistinguishable and homogenous. We know that there are many ways to generate an ideal single-photon source. Laser attenuated single-photon sources, atomic single-photon sources, molecular single-photon sources, quantum dot single-photon sources, etc. have all made great progress in preparation. Here we mainly introduce the method of using single quantum dot pulses to excite single photon. It has forward-looking applications in the quantum region. In the 1990s, it was discovered that quantum dots have the photon bunching effect and can emit single photon. It has been proved in 2000 that semiconductor single quantum dot can adjust the process of single photon generation by anharmonicity through multiple exciton transitions [29]. In 2014, the group of the University of Michigan obtained an Indium Arsenide (InAs)/Gallium Arsenide (GaAs) quantum dot single-photon source that can work at room temperature, and finally measured g⁽²⁾(0) = 0.29. The newest single-photon source based on quantum dots researched internationally, with higher performance and gradually approaching the ideal single-photon source, has also opened up a new technological path to integrated single-photon source.

With the single-photon source that can be integrated on a chip, we can get a variety of applications by embedding the single-photon emitters in the photon circuits. Photon routing using reconfigurable integrated circuits is a key function of quantum information processing. Single -photon router is based on two adjustable waveguides whose spacing can be changed by the external voltage. The quantum dot emitting single photon is embedded in one of the waveguides. The coupling strength of directional couplers can be adjusted by an integrated electrostatic actuator that leads to mechanical deformation by capacitive driving. Papon et al. [30] performed high extinction routing on a single photon emitted by a single quantum dot in 2019. As shown in Figure 3(a), the photons emitted by each quantum dot will be distributed to two output ports. Unlike the thermo optical method, mechanical motion is decoupled from quantum dots, which indicates that the single photon emitter will not be influenced and confirms a good property of the quantum dot.

Figure 3:

Applications to photon, charge, and phonon manipulation. (a) False-color scanning electron micrograph of the single-photon router. The red spot marks the approximate position of the quantum dot used for the experiment. The inset shows a zoom-in of the central section of the device where the waveguides have been highlighted in blue [30]. (b) Schematic drawing of the optomechanical device about charge control, and (c) corresponding circuit. The carbon nanotube, marked in brown in the model [35]. (d) Schematic of piezoelectric coupling to the modes of a high-overtone bulk acoustic wave resonator. The sine curve in the figure represents the longitudinal part of the wave function, and it has a wavelength λ = 2h/l on the cylindrical mode volume defined by the AlN disc and the sapphire substrate below. The transverse energy density profile of sl,0(x⃗) is plotted in 3D, showing the effective confinement of energy inside the mode volume [17].

Similar combination of single-photon emitters and directional couplers can also realize quantum beam splitter. The beam splitters implemented on the chip using directional couplers (DC) is another key component of the integrated linear quantum optical circuit [23], and then optical control may be the optical characteristic required for effective quantum information processing (QIP) applications [31, 32]. The proposed proof-of-concept devices are compact, easy to manufacture and versatile to combine with various on-chip photonics structures, which represents a crucial progress in on-chip quantum circuits field. It represents an important step in a reconfigurable integrated quantum optical circuit with an embedded single-photon source.

Quantum photonic integrated circuits are promising new type of semiconductor technology, where single-photon emitters are embedded and the evolution of quantum states of the emitted photons from those emitters are adopted to manipulate information. Good quality single-photon emitters are usually embedded in nanocavities, however, energy mismatch between the cavities and the emitters is usually inevitable, which sets challenges to the implementation of circuits to simultaneously manipulate single photons from remote emitters. However, the inevitable energy mismatch between remote cavities and points, as well as the difficulty of coupling with the waveguide network, hinders the implementation of circuits that simultaneously manipulate single photon generated from remote sources. So in order to obtain high purity and coherent single photons from quantum dots, we need spectral filtering to select single exciton transitions. Wavelength-tunable filter [33] on a chip integrated with a single photon source can also be implemented using nanomechanical motion. In addition, multiple tunable quantum dot sources are integrated in the photonic circuit [22]. The electrically tunable single photon source is combined with the mechanically reconfigurable photonic crystal element. This platform can be applied to multi-cavity quantum electrodynamics nodes in the near future.

In addition to the above achievements in the manipulation of single photon, there have been some interesting applications in recent years for achieving quantum ground states at room temperature. The preparation of the mechanical system of the quantum ground state at room temperature is a key challenge in the study of quantum photomechanics. In 2020, Guo et al. [34] combined integrated nanophotonics with phononic bandgap engineering. This new microchip technology can feedback cools the mechanical resonator from room temperature to about 1 mK. It proved a single-photon cooperativity of 200. It creates the real quantum state of the macroscopic system, and paves the way for the application of a new generation of quantum limited mechanical sensors.

Besides the manipulation of photons, there are also several hybrid systems for controlling charges. Compared with the material silicon, carbon-based materials (such as diamond, carbon nanotubes and graphene) have excellent properties, such as low quality, high Young’s modulus, high thermal conductivity, hydrophobic surface, and customizable electronic configurations. Materials make NEMS have broader application prospects [36–39]. Because of their superior mechanical and electrical properties, they are often used to achieve a variety of electronic manipulation in NOEMS. Here we take the widely used carbon nanotubes as examples and introduce some typical applications in recent years. The suspended carbon nanotube is a high-quality resonator. As a narrow-gap semiconductor, carbon nanotube quantum dots are composed of tunnel barriers at both ends and a Coulomb island with a very small capacitance value near the middle, which contains a very small amount of electrons. Energy is composed of electric potential energy and Coulomb energy of interaction between electrons. When an electron increases or decreases on Coulomb island, its energy increases by e²/C. The activation energy of e²/C is required for a single electron to enter or leave Coulomb island. Under extremely low temperature and small bias voltage, the electrons in the conductor do not have the energy of e²/C, so the electrons cannot cross the Coulomb island. This phenomenon is called Coulomb blockade. The potential energy and total energy of the Coulomb island can be changed by adding a gate voltage. Under a certain gate voltage, the minimum energy of the Coulomb island total charge Q = Ne and Q = (N − 1)e is degenerate. And the density of states gap disappears. And the phenomenon that a single electron tunnels through the Coulomb Island occurs. It is called the single electron tunneling effect.

In recent years, there have been more and more NEMS systems based on suspended carbon nanotubes. There are many experiments using quantum dots and superconducting microwave cavity coupling. The simplified schematic and circuit model shown in Figure 3(b) and (c) reveal typical quantum capacitance mediated carbon nanotube optomechanics [35]. In addition, carbon nanotubes can also define single-electron transistors (SET) through the tunnel barriers at both ends and the Coulomb islands near the middle [40]. The two related SET states are configurations with and without excess electrons. The bending vibration of the nanotube regulates the electric potential experienced by the SET, which causes the current to change with displacement. When the SET is coupled with the phonon cavity, strong interaction can be achieved between electrons and phonons. Under strong coupling conditions, it will produce selfsustained coherent mechanical oscillations.

Manipulation of phonon also has become a promising research field for optical signal processing, sensing applications and emerging quantum technologies, which also has vital applications in quantum information. A series of experiments in the field of nano-electro-mechanics show that in the quantum field, the control of linear mechanical systems can be achieved through qubits, such as coupling between a superconducting qubit and a mechanical resonator with great robustness and high coherence. Among them, the mechanical states of qubit coupling mainly include bulk acoustic wave (BAW) [41, 42] and surface acoustic wave (SAW) [43–45]. Under the physical mechanism of piezoelectric excitation, they are mostly used as sensors, and then deal with long-distance quantum information transduction. BAW resonator sensors which are propagating in the elastic solid with superior sensitivity are mainly used in the high-performance measurement device. In contrast, since the surface acoustic waves on the surface of piezoelectric crystals excited by interdigital transducers were proposed in the 1960s, the application of new surface acoustic wave devices has a history of more than 40 years. The most widely used are surface acoustic wave filters, including radio frequency and mid-band pass filters, especially communication filters. The second is the surface acoustic wave sensor. Because the propagation speed and attenuation of the surface acoustic wave are closely related to the parameters of the propagation environment and medium, the use of surface acoustic wave devices to make sensors has high sensitivity. Therefore, it is widely used in the fields of automation, biomedicine, chemical industry, environmental monitoring, military, antiterrorism, and antidrug.

In recent years, the manipulation of single phonon has generally been achieved through coupling experiments with superconducting qubits, or with purely mechanical systems. First, a typical coupling experiment between BAW and superconducting qubits [17] is shown in Figure 3(d). A high-frequency BAW resonator is strongly coupled with superconducting qubits through piezoelectric transduction in 2017. The qubit and mechanical coherence time obtained by measurement is only about 10 μs, and the system’s cooperativity is 260. The work demonstrated the quantum control and measurement of single-quantum-level gigahertz phonons. In 2018, by greatly improving the quantum operation speed and mechanical coherence time, Chu et al. [46] studied the Fock state with a definite number of phonons. They demonstrated the controlled generation of multiphonon Fock states in a large bulk acoustic wave resonator. Secondly, they also performed Wigner tomography and state reconstruction. It is found that the phonon mode has a lifetime of T₁ = 64 ± 2 μs, a Ramsey decoherence time of T₂ = 38 ± 2 μs and an echo decoherence time of T_2e = 45 ± 2 μs. Because their acoustic resonators greatly increase the coherence time, it is possible to demonstrate the selective coupling of superconducting qubits to various phonon modes. Through this paper, they confirmed that circuit quantum acoustic dynamics can perform complex quantum control of large mechanical objects and opened up the possibility of using acoustic modes as quantum resources. In addition, the coupling of SAW and superconducting qubits also demonstrates the complete quantum control of the mechanical state of the macromechanical resonator [47]. Wigner tomography [48–53] can map the non-classical superposition of 0 and 1 phonon Fock states.

The manipulation of single phonons in the above cases is only achieved by coupling superconducting qubits [54–56], while optical control is limited to the generation of quantum states in the bipartite system [57–59]. Therefore Hong et al. [60] immediately demonstrated the all-optical quantum control of a purely mechanical system, creating single-quantum-level phonons in 2017. They have combined the opto-mechanical control of motion and single-phonon counting technology [61] to generate the phonon Fock state probabilistically from a nanomechanical device. Then three years later, MacCabe et al. obtain a 1.5 s life time of phonons in microwave frequencies with nanoscale silicon acoustic cavities [62], which provides a possibility for future applications of quantum memory based on hybrid superconducting quantum circuites.

4 Applications to information processing

By mechanically moving or deforming the photonic structure, various applications including tunable modulators, couplers, transducers, routers, and switches have been proposed. In this section, the field of mechanical tunable photonic devices with on-chip integrated NEMS actuators will be classified and reviewed based on the configuration of photonic devices. In general, applications to information processing are mainly implemented in different configurations including nanobeam cavity, photonic waveguide, and ring/disk resonators. Here, we exemplify the application of NOEMS in different configurations in the classical optical field.

Here we first introduce the one-dimensional (1D) optical waveguide. Silicon-based optical waveguides are widely used in various classical and quantum optical experiment platforms. Compared with the free-space optical NEMS, the operation of confining light to the chip through the waveguide greatly reduces the optical mode size. While achieving low-loss coupling, it greatly reduces the difficulty of monolithic integration with other optical components. Free-space NEMS optomechanical coupling experiments usually require higher-cost hybrid packaging. The research of NEMS in the field of integrated optics neutralizes the advantages of the two, not only realizes the compact and low-cost packaging of integrated waveguides, and greatly reduces losses; it also realizes the low power, wavelength insensitivity, and independence of switches by mechanically moving the waveguides. In hybrid systems with photonic crystal waveguides as the main body of optical–mechanical coupling, comb static actuators are often used as drivers to generate electrostatic force to drive the waveguides. Comb drivers supported by a beam suspension firmly connected to the waveguide are the movable structures. The actuator is driven by an electrostatic force which is one of the most widely used MEMS/NEMS actuators. The structure of the waveguide system of experimental constructions for different purposes is also different, generally divided into two categories: one is the end-to-end system structure arranged longitudinally along the waveguide axis; the other is the system using two or more waveguides arranged horizontally structure. First, several basic electrostatic force-driven end-coupled waveguide structures have been presented. There are typical waveguides with a gap between the end and end, waveguides with an offset along the longitudinal direction, and waveguides where the ends are inclined at an angle.

In the 1D waveguide structure, the movable directional coupling waveguides are mainly used in the silicon photonic switches [67–70]. This type of optical switch has extremely high scalability, and there is hardly loss in the OFF state. With the improvement of design and manufacturing process, the loss can be further reduced, and the size of optical switches can be further large. With the development of large-scale integrated photonics, the integration density of silicon photonic switches has become higher, and the number of ports has increased from 50 × 50 to 128 × 128. Until 2019, Seok et al. [18] further scaled optical switches to 80 × 80 switch blocks with 240 × 240 ports. They reduced the loss significantly by reducing the width of the waveguide. The maximum on-chip loss of the switch prepared on a 4 × 4 cm chip is 9.8 dB, the switch on-off ratio is 70 dB, and the switching time is less than 400 ns. The integrated photonic switch reported has also become the largest switch reported so far and the switch with the lowest port loss count ratio. In conventional optical switches, we use an electromechanical driver to change the gap between two silicon waveguides to implement the conversion, where a large gap size requires a high driving voltage. Whereas, in high-density optical switches driven by CMOS circuits [63] illustrated in Table 1(a), the light field is restricted in subwavelength structures that facilitates a stronger response of the applied electromechanical field and reduces the driving voltage [71, 72], which has promoted the development of CMOS-integrated optical devices. In addition to different structures, previous electrostatically driven optical switches have also been implemented in optical waveguides of different materials, such as silicon-on-insulator (SOI) [73], silicon-oxynitride (SiON) [74], polymer [75], and gallium arsenide (GaAs) [76].

Table 1:

Applications to classical information transduction.

Configuration	Photonic crystal waveguide	Nanobeam cavity	Photonic crystal cavity	Ring/disk resonator
Principle	Evanescent coupling	Cavity deformation	Cavity deformation	Coupling strength tuning
Application	Routing	Optical-microwave signal transductor	Optical signal processing	Switchable filter
	Displacement sensor	Resonance control	Resonance control	Bandwidth tunable filter
	Phase modulator	Switch	Switch	Switch
Example
	(a) [63]	(b) [64]	(c) [65]	(d) [66]

In addition to traditional silicon-based optical waveguides, photonic crystals, as a popular artificial periodic dielectric structure used to transmit photons, have also been widely used in the construction of hybrid NOEMS in recent years. From the perspective of material structure, photonic crystals are artificially designed and manufactured crystals with periodic dielectric structures on the optical scale. It is periodically arranged by media with different refractive indices. And it has a photonic band gap, which means that waves of a certain frequency range cannot propagate in this periodic structure, that is, the structure itself has a “forbidden band”. Due to its unique properties, photonic crystals have unique advantages in photonic integrated devices. Many photonic components based on traditional waveguides can also be implemented by constructing different photonic crystals, such as photonic crystal waveguide filters and couplers. The way of introducing defects into photonic crystals to form photonic crystal cavities provides numerous excellent experimental results for information processing in the field of classical physics. Photonic crystal cavities can generally be divided into three types: 1D [77], two-dimensional (2D) [78], and three-dimensional (3D) cavity. 1D photonic cavity (also called nanobeam cavity) is a Fabry–Perot-like resonator constructed through two photonic Bragg mirrors. The 2D photonic cavity is formed by inducing defects in the planar photonic crystal. Since 3D cavities are so difficult to manufacture and characterize on the chip that are rarely studied nowadays.

The ideal hybrid NOEMS device is a combination of an optical device that is extremely sensitive to mechanical deformation and an electromechanical device that can cause greater deformation through a proper voltage. In the part of electromechanical coupling, the requirement of large voltage-induced displacement has been difficult to meet. In order to solve this problem and realize electromechanical device with higher sensitivity and wider tuning range, a series of NOEMS based on 1D nanobeam photonic crystals have emerged. There are many interesting construction methods for this one-dimensional structure. Among them, a novel NOEMS can be constructed by spliting one nanobeam horizontally or vertically, and then mechanically moving a part of the nanobeam in different directions, and the approach that moving two adjacent nanobeams by electrostatic force is also generally used in optomechanical coupling configuration. In the field of classical information transduction, devices are generally deformed by means of electrostatic force or piezoelectric force. The electrostatic force is generated by the voltage-induced polarization in the material. They do not require any special material properties. For example, the NEMS components are integrated with the opto-electro-mechanical crystal cavity [20], through electrostatic tuning the displacement of the additional tuning beam in the near field of the opto-electro-mechanical cavity is controlled. Thus, the optical mode is affected, and the optomechanical coupling rate is changed. However, electrostatic actuation is limited by a certain combination of actuation range, sensitivity, device footprint, and speed. In the context of piezoelectric photonic integration, these limitations can be overcome. By manipulating the piezoelectric optomechanical tunable cavity and waveguide, the tuning and reconfiguration of nanophotonic components are realized.

As shown in Table 1(b), Jiang et al. [64] successfully obtained an efficient piezoelectric actuator for widely tunable nanophotonics at CMOS-level voltages in the classical domain in 2020. This system constructs the waveguide-zipper coupling region, and innovatively adds nanobender attached to the zipper cavity as a compact piezoelectric actuator, which can convert tens of nanometers per volt. Then they create the bending of piezoelectric nanobeams by using the uneven electric field from the submicron electrodes. And it becomes a widely tunable nanophotonic component.

As illustrated in Table 1(c), 2D photonic crystal cavities also have various applications in the field of sensing. Among them, with the increasing demand for displacement sensing in experiments such as acceleration measurement and atomic force microscope, there are more and more researches on using 2D photonic crystal cavities to construct integrated displacement sensing devices. While we are pursuing higher resolution and bandwidth on the optical platform, on-chip integration is a must. Only in this way can we meet our requirements for low-cost and compact parallel equipment. In recent years, many optomechanical displacement sensing devices that integrate on-chip detection, excitation and optical transmission functions have emerged. They are proven to be excellent force and displacement sensors [65]. Due to their subnanometer resolution and manufacturing based on semiconductor processing technology, they have the potential to integrate a large sensor array on a single chip for high-resolution and high-throughput atomic scale imaging.

Different from the method of photonic crystal thin film construction in the above article, Winger et al. [79] proposed in 2011 a mechanical degree of freedom coupled with a high-Q photonic crystal cavity, and through a wide range, fast electronic tuning of the opto-electro-mechanical integration nanoscale structure. This new type of microsensor provides a new idea for the effective conversion of microwave and light signals, and also provides a possibility for low-noise optical readout. This article proposes a slotted-waveguide photonic crystal cavity. The air gap formed between two parallel individual photonic crystal films serves as a waveguide defect to form an optical cavity. The two pairs of metal contacts on each membrane are used as capacitive electrostatic actuators, which can change the width of the air gap and electromechanically control the movement of the membrane. When the applied voltage passes through the capacitance gap, electrostatic force is generated to cause the capacitance to shrink, which causes the resonance frequency of the cavity to blue shift. The applications of this device range from classical wavelength filters and low-power optical modulators to quantum-limited force sensors.

A well-known microoptical resonator for light control is a microring/disk resonator, also known as a whisper-gallery mode (WGM) resonator. The Q factor of ring/disk resonators made of silicon/silicon dioxide materials can exceed 10⁸. As shown in Table 1(d), a classic wavelength selective add/drop filter is presented [80], with four ports called input, pass, add, and drop, respectively. A wavelength selective switch using a silicon microring resonator is reported, in which the coupling between the bus and the microring can be changed by an electrostatic microcomb actuator. The microring cavity is suspended in the air and is connected to an actuator with a low loss suspension arm. All components of the device are fabricated on the top layer of a SOI wafer using a single electron beam mask process, which portends a potential to combine with other innovative silicon waveguide devices.

In addition to structural innovation, the development of new materials is another attractive research direction. As we all know, plasma equipment can be embedded in photonic circuits as various types of photonic modulators [81, 82]. The manufacturing process of this kind of plasmonic components is also very mature [83]. Similar to the mechanical modulation of silicon photonic devices discussed above, plasma devices can also achieve on-chip mechanical modulation through electrostatic methods. For example, phase modulators based on tunable metal–insulator–metal gap plasmons have been reported [84]. The surface plasmons at the gold-air interface are excited by the free-space laser focused on the grating coupler. Then it is modulated in the suspended Au bridge array. Finally, it couples with the output beam of the slot coupler and interferes with the reference beam. When a voltage is applied between the suspended gold bridge and the gold substrate, the gold bridge is deformed and bent downward, so that the gap between the gold layers is reduced. The phase velocity of the surface plasmon is extremely sensitive to the gap change, so a large phase modulation can be achieved through a small mechanical movement, thereby obtaining the phase information of the output light. Compared with traditional Si photonic devices, the modulation depth of the plasmons modulator introduced above is excellent.

5 Applications to quantum information processing

In the past few decades, people have not been satisfied with the various applications of NOEMS confined to the classical field, but have stepped into the quantum field [85]. With the development of integrated photonics and nanophotonics, nanoscale manufacturing technology provides a platform for conducting quantum optical experiments directly on a chip, effectively replacing large optical equipment. Quantum state processing, transmission, and storage could be realized, and the goal of constructing quantum information network would be finally achieved. So far, great progress has been made in both experiments and theories in this field. In this chapter, we will explore the novel applications of NOEMS in quantum information networks. Various NOEMS not only have higher and higher microwave-to-optics conversion efficiency in the classic field in the past three years, but also have more extensive applications in the fields of optical switches, routers, and transducers. Moreover, the development prospects of related applications in the quantum field are also bright. We believe that these compact NOEMS hybrid devices have important untapped potential in electro-optic modulation, quantum microwave to optical photon conversion, sensing, and microwave signal processing.

With the development of cavity quantum mechanics, people began to study the experimental work of embedding high-Q mesoscopic mechanical oscillators into microwave and optical cavities. The conversion of quantum states from microwaves to optical domains or from optical domains to microwaves has aroused great interest. Platforms such as superconducting circuits [86], spins in solids [87] and quantum dots [88] can process quantum information locally. Microwave photons naturally operate in the gigahertz frequency domain, but the long-distance transmission of gigahertz radiation is relatively lossy and inelastic to environmental noise. In practical situations, this limits the length of the subcooled microwave waveguide to tens of meters [89]. However, optical photons can be transmitted through fibers which are different from microwave photons, making them suitable for long-distance quantum communications. The current experimental techniques for microwave upconversion mainly include: nonlinear electro-optical coupling, nonlinear magneto-optical coupling, and multilevel systems and the interaction between photons mediated by mechanical or piezoelectric elements [90, 91]. So far, the optomechanical method has been proven to be the most effective, reaching a record high photon conversion efficiency of 47%.

In the early years, people used a mechanical resonance film sensor to measure the radio frequency voltage signal [96], which can directly transmit nanovolt-level electrical signals from the magnetic resonance coil [97] to the low-loss optical field on the optical fiber. With the continuous improvement of micronano technology, the quantum field has been able to realize the coupling between the electrical signal of 4 GHz and the optical photon of 200 THz with the nanomechanical transducer shown in Figure 4(b) [92]. A transducer operating at such a high mechanical frequency can reach a mechanical quantum ground state at a temperature of about 300 mK, which is easily obtained in a dilution refrigerator. More importantly, the transducer is fully compatible with superconducting circuits, which provides a potential way to connect photon qubits and superconducting circuits. After achieving the upconversion of microwave to optical signals, in 2014, Andrews et al. [98] demonstrated bidirectional transduction of classical information between microwave and optical signals, which is based on a SiN thin film capacitively coupled to a superconducting LC circuit through the radiation pressure of photons. And the overall effective microwave-optical conversion efficiency is around 10% added with 10³ quanta noise.

Figure 4:

Applications to quantum information processing. (a) Block diagram of the piezo-optomechanical transduction process, indicating the electrical, mechanical, and optical modes, relevant frequencies (ω_MW, ω_LC, ω_m, ω_o, ω_pump), decay channels ((1 − η_e)κ_e, γ_m, κ_i), cooperativities (C_EM, C_OM), and electrical and optical coupling efficiencies (η_e and η_o). (b) Scanning electron micrograph of the device (angled view) showing the mechanically suspended AlN optomechanical crystal (blue) with aluminum electrodes (yellow) and the AlN photonic circuit (red, rib waveguide and grating couplers) [92]. (c) Microscope image of the microwave-to-optics transducer devices: The structures are comprised an interdigital transducer (IDT, in gold, cf. upper inset), which spans several optomechanical devices for ease of fabrication [93]. (d) Silicon photonic microwave-to-optics converter. Scanning electron micrograph (SEM) of the device showing the microwave lumped element resonator with an inductively coupled feed line, the photonic crystal cavity, and the optical coupling waveguide fabricated on a fully suspended 220 nm thick silicon-on-insulator device layer [94]. (e) SEM of one piezo-optomechanical transducer [19]. (f) Electrical circuit representation of the integrated qubit and transducer device [95].

At present, with the development of quantum technology, there are more and more related achievements in up conversion and bidirectional conversion between microwave and optical signals. The continuous exploration of different materials, different structures, and different experimental conditions all provide directions for obtaining higher efficiency microwave-to-optical conversion. For quantum applications, the conversion must be both effective and in the form of minimal classical noise. Although the use of mechanical transducers has proven effective conversion, so far, they have all operated under a considerable thermal noise background. Forsch et al. [93] overcomed the limitation of large thermal noise background, and proved the coherent conversion between GHz microwave signal and optical communication frequency band with thermal background less than one phonon, as shown in Figure 4(c). They coupled surface acoustic waves driven by resonant microwave signals to an optomechanical crystal with a 2.7 GHz mechanical mode. The experiment initializes the mechanical mode to its quantum ground state, which allows them to perform the transduction process with minimal additional thermal noise while maintaining opotomechanical cooperativity >1, so that the microwave photons mapped into the mechanical resonator can be effectively upconverted to the optical domain. On the integrated superconducting cavity piezoelectric optomechanical platform, piezoelectric-mechanical and optomechanical coupling is realized through a hybrid interface. This kind of hybrid quantum system is the key to realizing distributed quantum network, and it is also a new exploration of gigahertz phonon-mediated microwave photon entanglement and quantum sensing. Han et al. [99] used large piezoelectric-mechanical synergy (C_em ∼ 7) and pulsed optical pump enhanced optomechanical coupling to realize microwave (∼10 GHz) and photonics (∼200 THz) effective bidirectional conversion. In 2020, Arnold et al. [94] published a work to realize the conversion of microwave and telecom photons in a 1D nanobeam system with zipper cavity as shown in Figure 4(d). In this work, authors proposed a scalable solution to interface the microwave and optical domains. The realization of this work relies on the radiation pressure interaction mediated by the femtometer-scale motion of two silicon nanobeams. The fully integrated coherent transducer has a bidirectional conversion efficiency of 1.2% (135%) at milli-Kelvin temperature. Without the relevant optomechanical gain, the system can achieve a total (internal) pure conversion efficiency of up to 0.019% (1.6%), laying the foundation for the noise-free operation of future qubit compatible platforms.

As shown in Figure 4(e), Jiang et al. [19] systematically solved efficient interconversion of both classical and quantum information between microwave and optical signals with an on-chip piezoelectric optical transducer. The device could be operated as a classical modulator where an optomechanical crystal was integrated with a mechanical waveguide and the optical resonance frequency of the optomechanical crystal could be modulated by a microwave through the mechanical waveguide. On the other hand, the device could also act as a quantum transducer. As a laser with a detuned frequency equal to the mechanical resonate frequency from the optical resonate frequency exerted on the optomechanical crystal, interactions between photons and the mechanical motion of the device are introduced. Then bidirectional transduction between optical and microwave photons could be implemented through the device, and the authors have demonstrated bidirectional conversion with quantum efficiency up to 10⁻⁵ using the red-detuned laser pump and 5.5% with the blue-detuned pump. As shown in Figure 4(f), in 2020, the frequency excitation of superconducting qubits will finally achieve the microwave frequency conversion of photons to maintain the fragile quantum state which is different from the above experiments [95]. They achieved this goal by using a nanomechanical resonator in the middle, which converts the electrical excitation of the qubits into individual phonons through piezoelectric interaction, and then converts the phonons into photons through radiation pressure. The author records the quantum Rabi oscillations of qubits by detecting single photons of light emitted on the optical fiber, thus proving the process of generating photons from qubits. With improvements in equipment and external measurement settings, such quantum sensors can be used to implement new hybrid quantum networks and distributed quantum computers.

Besides 1D NOEMS hybrid system, many interesting 2D and 3D cavity structures have also emerged that are dedicated to quantum microwave-to-optics conversion last year. In 2020, Ren et al. [100] proposed a 2D optomechanical crystal resonator. It is a periodically patterned quasi-two-dimensional plate structure with phononic and photonic band gaps, which contains a quasi-two-dimensional snowflake optomechanical cavity. The resonator can achieve a large cooperativity C and a small effective bath occupancy n_b, resulting in a quantum cooperativity C_eff = C/n_b > 1 under continuous wave optical driving. This is achieved by using a 2D phonon band gap structure to accommodate the optomechanical cavity, while isolating certain acoustic modes in the band gap, while allowing heat dissipation through phonon modes outside the band gap. This achievement paved the way for a variety of applications that require quantum coherent optomechanical interaction, such as transducers capable of bidirectionally converting quantum states between microwave frequency superconducting quantum circuits and photons in optical fiber networks. Srinivasan et al. [101] demonstrated a transducer that combines high-frequency mechanical motion and a microwave cavity in 2020. The system consists of a 3D microwave cavity and a GaAs optomechanical crystal placed in the maximum microwave electric field. This allows the microwave cavity to drive a mechanical breathing mode of one gigahertz frequency in the optomechanical crystal through the piezoelectric effect, and then use the telecom optical mode to read out. GaAs optomechanical crystal is a good candidate material for the transduction of low-noise microwaves to telecommunications because it has previously been cooled to the mechanical ground state in a dilution refrigerator. In addition, the 3D microwave cavity structure can naturally be extended to couple superconducting qubits and create hybrid quantum systems.

From all the splendid work of NOEMS in optical and microwave frequency transduction in recent years, we could extract that GaAs, aluminum nitride (AlN), and lithium niobate (LiNbO₃) are commonly used materials in integrated piezoelectric devices. As a comparison, the piezoelectric coupling coefficient in AlN is around 3–7%, and LiNbO₃ device could research as high as 30%, while that is only around 0.02–0.03% in GaAs devices. However, it is difficult for LiNbO₃ devices to attain high mechanical and optical quality factors to ensure a high optomechanical cooperativity coefficient. Hence, as a compromise, AlN devices appear to be the optimal solution to ensure both piezoelectric and optomechanical performance. Next, we summarize transducers of different materials and properties in Table 2, so that we can more clearly analyze and summarize the development of quantum information in the direction of change in recent years.

NOEMS devices play critical roles in manipulation and routing of single photons not only at a node of quantum networks, but also at multiple nodes at a distance, which makes quantum networks more accessible for applications. In a fully functional quantum network, photons in the near infrared band are adopted as the flying qubits to transmitting information in a long distance while photons in the microwave band are used to manipulate the information at a node of the networks. Then NOEMS devices provide a typical solution for the bidirectional information transfer between optical single and microwave signals. The on-chip approach above merges integrated photonics with microwave nanomechanics and is completely compatible with superconducting quantum circuits, enabling bidirectional quantum states transfer. Whether it is a single photon manipulation within a network node, or a multi-node, long-distance quantum information network, it provides more possibilities for NOEMS to develop and grow in a wider field in the future.

In the process of quantum physics research, there is an interesting phenomenon called the Casimir effect [102]. The Casimir effect is a physical force acting on the boundaries of a confined space due to quantum zero-point fluctuations of the electromagnetic field, which manifests as an attraction force between two uncharged, perfectly conductive parallel plates. The Casimir force was first proposed by Casimir [103] in 1948, which was convincingly confirmed by many experiments in the following decades. With the continuous improvement of micro- and nano-manufacturing technology, the Casimir effect has received extensive attention and in-depth research in the field of NOEMS. When the size of the experimental system and the distance of interaction are considered, the measurement objects are mainly divided into macroscopic and microscopic systems. A typical macroscopic system is generally composed of parallel plates or a combination of sphere and plate [104, 105]. The size of the object for measuring the Casimir force is generally a few centimeters, and the distance between the objects is on the order of micrometers. When we step into the microscopic field, many experiments using MEMS/NEMS technology to characterize the Casimir force have emerged [106–110]. The dynamic Casimir effect based on the superconducting quantum interference devices (SQUID) [111–113] are also studied. In addition, Fong et al. [114] studied strong phonon coupling through vacuum fluctuation based on NOEMS in 2019. All these excellent theoretical and experimental results of the Casimir effect lay a foundation for future studies of energy transport in quantum vacuum, and bring practical implications into the field of NOEMS.

6 Outlook

In this article, we mainly listed and analyzed various novel experiments and potential applications in the NOEMS field in the past two years. It is not difficult to see that various components are being continuously reduced in size to adapt to the current trend of integration. Moreover, reducing the size to the nanometer level is not only good for reducing the footprint and reducing energy consumption, but more importantly, the new quantum effects it brings, which can provide more opportunities for the development of nanophotonics in the future.

Under the guidance of fascinating theories, more and more novel applications are emerging, mainly in optical switching, routing, and sensing. Especially in the application of quantum information, there is a broader development prospect [115, 116]. Based on quantum dots, continue to optimize applications such as optical routing, and gradually design single-photon sources [117]. Quantum dots, as one of the current hot research directions, have emerged many reconfigurable quantum photonic circuits or systems based on the source integration of them. This hybrid system that integrates quantum emitters, optical routing, single-photon sources, and other components also provides conditions for realizing more cutting-edge quantum sensing and precise measurement. We hope that NOEMS can be further researched and tested to penetrate its meaningful applications into more fields.