Directional amplifiers are crucial nonreciprocal devices in both classical and quantum information processing. Here we propose a scheme for realizing a directional amplifier between optical and microwave fields based on an optomechanical system with optical gain, where an active optical cavity and two passive microwave cavities are, respectively, coupled to a common mechanical resonator via radiation pressure. The two passive cavities are coupled via hopping interaction to facilitate the directional amplification between the active and passive cavities. We obtain the condition of achieving optical directional amplification and find that the direction of amplification can be controlled by the phase differences between the effective optomechanical couplings. The effects of the gain rate of the active cavity and the effective coupling strengths on the maximum gain of the amplifier are discussed. We show that the noise added to this amplifier can be greatly suppressed in the large cooperativity limit.
We model optomechanical systems as linear optical amplifiers. This provides a unified treatment of diverse optomechanical phenomena. We emphasize, in particular, the relationship between ponderomotive squeezing and optomechanically induced transparency, two foci of current research. We characterize the amplifier response to quantum and deliberately applied fluctuations, both optical and mechanical. Further, we apply these results to establish quantum limits on external force sensing both on and off cavity resonance. We find that the maximum sensitivity attained on resonance constitutes an abso…
Cavity optomechanical system involving an optical parametric amplifier (OPA) can exhibit rich classical and quantum dynamical behaviors. By simply modulating the frequency of the laser pumping the OPA, we find two interesting parameter regimes, with one of them enabling to study quantum-classical correspondence in system dynamics, while there exist no classical counterparts of the quantum features for the other. For the former regime, as the parametric gain of OPA increases to a critical value, the classical dynamics of the optical or mechanical modes can experience a transition from the regul…
We theoretically investigate optical detection of a weak classical force acting on a free particle in a dissipative coupling optomechanical system with a degenerate parametric amplifier (PA). We show that the PA allows one to achieve the force sensitivity far better than the standard quantum limit (SQL) over a broad range of the detection frequencies. The improvement depends on the parametric gain and the driving power. Moreover, we discuss the effects of the mechanical damping and the thermal noise on the force sensitivity. We find that the robustness of the force sensitivity much better than…
The sensitivity of future gravitational wave interferometers is expected to be limited through-out the detection band by quantum vacuum fluctuations, which can be reduced by quantum non-demolition methods such as squeezed vacuum injection. However, optical losses in the readout chainseverely limit the effectiveness of such schemes. We propose an optomechanical device to be installedat the output of the detector that mitigates the effect of readout loss, thus allowing the detector tobetter exploit quantum noise evasion schemes.
We investigate the effect of a degenerate optical parametric amplifier (OPA) placed inside an optomechanical cavity on the steady-state entanglement of two cavity modes, which jointly interact with a mechanical resonator. Two cavity modes are respectively driven at the red and blue sideband associated with the mechanical resonator, which generates entanglement between them in the limit of resolved sideband. The OPA gives rise to single-mode squeezing of the cavity fields, which results in significant improvement of the two-mode entanglement. It is found that an optimal nonlinear gain of the OP…
High-quality microwave amplifiers and notch-filters can be made from microwave optomechanical systems in which a mechanical resonator is coupled to a microwave cavity by radiation pressure. These amplifiers and filters rely on optomechanically induced transparency (OMIT) and absorption (OMIA), respectively. Such devices can amplify microwave signals with large, controllable gain, high dynamic range and very low noise. Furthermore, extremely narrowband filters can be constructed with this technique. We briefly review previous measurements of microwave OMIT and OMIA before reporting our own meas…
We propose how to achieve synthetic $\mathcal{PT}$ symmetry in optomechanics without using any active medium. We find that harnessing the Stokes process in such a system can lead to the emergence of exceptional point (EP), i.e., the coalescing of both the eigenvalues and the eigenvectors of the system. By encircling the EP, both non-reciprocal optical amplification and chiral mode switching can be achieved. As a result, our synthetic $\mathcal{PT}$-symmetric optomechanics works as a topological optomechanical amplifier. This provides a surprisingly simplified route to realize $\mathcal{PT}$-sy…
The investigation of the ultimate limits imposed by quantum mechanics on amplification represents an important topic both on a fundamental level and from the perspective of potential applications. We propose here a novel setup for an optomechanical amplifier, constituted by a mechanical resonator dispersively coupled to an optomechanical cavity asymmetrically driven around both mechanical sidebands. We show that, on general grounds, the present amplifier operates in a novel regime-- which we here call phase-mixing amplification. At the same time, for a suitable choice of parameters, the amplif…
Circulators and directional amplifiers are crucial non-reciprocal signal routing and processing components involved in microwave readout chains for a variety of applications. They are particularly important in the field of superconducting quantum information, where the devices also need to have minimal photon losses to preserve the quantum coherence of signals. Conventional commercial implementations of each device suffer from losses and are built from very different physical principles, which has led to separate strategies for the construction of their quantum-limited versions. However, as re…
We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is driven below its resonance, providing optical damping of the mechanical oscillations. We study the nonlinear coherent response of the mechanical oscillator in this setup. For large mechanical amplitudes, we find that the system can display dynamical multistability if the optomechanical cooperativity exceeds a critical value. This analysis relates standard opto…
Nonreciprocal transmission of optical or microwave signals is indispensable in various applications involving sensitive measurements. In this paper, we study optomechanically induced directional amplification and isolation in a generic setup including two cavities and two mechanical oscillators by exclusively using blue-sideband drive tones. The input and output ports defined by the two cavity modes are coupled through coherent and dissipative paths mediated by the two mechanical resonators, respectively. By choosing appropriate transfer phases and strengths of the driving fields, either a dir…
We experimentally study a fiber-based optical ring cavity integrated with a mechanical resonator mirror and an optical amplifier. The device exhibits a variety of intriguing nonlinear effects including synchronization and self-excited oscillation. Passively generated optical pulses are observed when the frequency of the optical ring cavity is tuned very close to the mechanical frequency of the suspended mirror. The optical power at the threshold of this process of mechanical mode locking is found to be related to quantum noise of the optical amplifier.
We consider an optical and mechanical mode interacting through both linear and quadratic dispersive couplings in a general cavity-optomechanical set-up. The parity and strength of an intrinsic quadratic optomechanical coupling (QOC) provides an opportunity to control the optomechanical (OM) interaction. We quantify this interaction by studying normal-mode splitting (NMS) as a function of the QOC's strength. The proposed scheme exhibits NMS features equivalent to a hybrid-OM system containing either an optical parametric amplifier (OPA) or a Kerr medium. Such a system in reality could offer an …
High-gain amplifiers of electromagnetic signals operating near the quantum limit are crucial for quantum information systems and ultrasensitive quantum measurements. However, the existing techniques have a limited gain-bandwidth product and only operate with weak input signals. Here we demonstrate a two-port optomechanical scheme for amplification and routing of microwave signals, a system that simultaneously performs high-gain amplification and frequency conversion in the quantum regime. Our amplifier, implemented in a two-cavity microwave optomechanical device, shows 41 dB of gain and has a …
We study the phonon dynamics in lattices of optomechanical resonators where the mutually coupled photonic modes are coherently driven and the mechanical resonators are uncoupled and connected to independent thermal baths. We present a general procedure to obtain the effective Lindblad dynamics of the phononic modes for an arbitrary lattice geometry, where the light modes play the role of an effective reservoir that mediates the phonon nonequilibrium dynamics. We show how to stabilize stationary states exhibiting directional heat currents over arbitrary distance, despite the absence of thermal …
We study the directional amplification of an optical probe field in a three-mode optomechanical system, where the mechanical resonator interacts with two linearly-coupled optical cavities and the cavities are driven by strong optical pump fields. The optical probe field is injected into one of the cavity modes, and at the same time, the mechanical resonator is subject to a mechanical drive with the driving frequency equal to the frequency difference between the optical probe and pump fields. We show that the transmission of the probe field can be amplified in one direction and de-amplified in …
We have realized a microwave quantum-limited amplifier that is directional and can therefore function without the front circulator needed in many quantum measurements. The amplification takes place in only one direction between the input and output ports. Directionality is achieved by multi-pump parametric amplification combined with wave interference. We have verified the device noise performances by using it to readout a superconducting qubit and observed quantum jumps. With an improved version of this device, qubit and preamplifer could be integrated on the same chip.
Directional transmission or amplification of microwave signals is indispensable in various applications involving sensitive measurements. In this work we show in experiment how to use a generic cavity optomechanical setup to non-reciprocally amplify microwave signals above 3 GHz in one direction by 9 decibels, and simultaneously attenuate the transmission in the opposite direction by 21 decibels. We use a device including two on-chip superconducting resonators and two metallic drumhead mechanical oscillators. Application of four microwave pump tone frequencies allows for designing constructive…
Quantum illumination is a quantum-optical sensing technique in which an entangled source is exploited to improve the detection of a low-reflectivity object that is immersed in a bright thermal background. Entangled sources between microwave and optical fields can be exploited to improve detection in microwave quantum illumination technique. We proposed a scheme to enhance the entanglement between the output fields of microwave and optical cavity by introducing optical parametric amplifier medium in cavity optomechanical system. We show that improving signal-to-noise ratio and decreasing error …
We realize and characterize a quantum-limited, directional Josephson amplifier suitable for qubit readout. The device consists of two nondegenerate, three-wave-mixing amplifiers that are coupled together in an interferometric scheme, embedded in a printed circuit board. Nonreciprocity is generated by applying a phase gradient between the same-frequency pumps feeding the device, which plays the role of the magnetic field in a Faraday medium. Directional amplification and reflection-gain elimination are induced via wave interference between multiple paths in the system. We measure and discuss th…
Directional amplifiers are an important resource in quantum information processing, as they protect sensitive quantum systems from excess noise. Here, we propose an implementation of phase-preserving and phase-sensitive directional amplifiers for microwave signals in an electromechanical setup comprising two microwave cavities and two mechanical resonators. We show that both can reach their respective quantum limits on added noise. In the reverse direction, they emit thermal noise stemming from the mechanical resonators and we discuss how this noise can be suppressed, a crucial aspect for tech…
We present a new theoretical framework to analyze microwave amplifiers based on the dc SQUID. Our analysis applies input-output theory generalized for Josephson junction devices biased in the running state. Using this approach we express the high frequency dynamics of the SQUID as a scattering between the participating modes. This enables us to elucidate the inherently nonreciprocal nature of gain as a function of bias current and input frequency. This method can, in principle, accommodate an arbitrary number of Josephson harmonics generated in the running state of the junction. We report deta…
Josephson-junction based parametric amplifiers have become a ubiquitous component in superconducting quantum machines. Although parametric amplifiers regularly achieve near-quantum limited performance, they have many limitations, including low saturation powers, lack of directionality, and narrow bandwidth. The first is believed to stem from the higher order Hamiltonian terms endemic to Josephson junction circuits, and the latter two are direct consequences of the nature of the parametric interactions which power them. In this work, we attack both of these issues. First, we have designed a new…
Directional amplification, in which signals are selectively amplified depending on their propagation direction, has attracted much attention as key resource for applications, including quantum information processing. Recently, several, physically very different, directional amplifiers have been proposed and realized in the lab. In this work, we present a unifying framework based on topology to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays. Specifically, we unveil a one-to-one correspondence between a non-zero topological invariant defined on the s…
We describe a new kind of phase-preserving quantum amplifier which utilizes dissipative interactions in a parametrically-coupled three-mode bosonic system. The use of dissipative interactions provides a fundamental advantage over standard cavity-based parametric amplifiers: large photon number gains are possible with quantum-limited added noise, with no limitation on the gain-bandwidth product. We show that the scheme is simple enough to be implemented both in optomechanical systems and in superconducting microwave circuits.
In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric non…
Optomechanical systems offer new opportunities in quantum information processing and quantum sensing. Many solid-state quantum devices operate at millikelvin temperatures -- however, it has proven challenging to operate nanoscale optomechanical devices at these ultralow temperatures due to their limited thermal conductance and parasitic optical absorption. Here, we demonstrate a two-dimensional optomechanical crystal resonator capable of achieving large cooperativity $C$ and small effective bath occupancy $n_b$, resulting in a quantum cooperativity $C_{\text{eff}}\equiv C/n_b \approx 1.3 > 1$ …
Accessing distinctly quantum aspects of the interaction between light and the position of a mechanical object has been an outstanding challenge to cavity-optomechanical systems. Only cold-atom implementations of cavity optomechanics have indicated effects of the quantum fluctuations in the optical radiation pressure force. Here we use such a system, in which quantum photon-number fluctuations significantly drive the center of mass of an atomic ensemble inside a Fabry-Perot cavity. We show that the optomechanical response both amplifies and ponderomotively squeezes the quantum light field. We a…
In this paper, we have investigated theoretically the influence of atomic collisions on the behaviour of a one-dimensional Bose-Einstein condensate inside a driven optical cavity. We develop the discrete-mode approximation for the condensate taking into account the interband transitions due to the s-wave scattering interaction. We show that in the Bogoliubov approximation the atom-atom interaction shifts the energies of the excited modes and also plays the role of an optical parametric amplifier for the Bogoliubov side mode which can affect its normal-mode splitting behaviour. On the other han…
Synthetic magnetism has been used to control charge neutral excitations for applications ranging from classical beam steering to quantum simulation. In optomechanics, radiation-pressure-induced parametric coupling between optical (photon) and mechanical (phonon) excitations may be used to break time-reversal symmetry, providing the prerequisite for synthetic magnetism. Here we design and fabricate a silicon optomechanical circuit with both optical and mechanical connectivity between two optomechanical cavities. Driving the two cavities with phase-correlated laser light results in a synthetic m…
Optomechanical quantum interfaces can be utilized to connect systems with distinctively different frequencies in hybrid quantum networks. Here we present a scheme of nonreciprocal quantum state conversion between microwave and optical photons via an optomechanical interface. By introducing an auxiliary cavity and manipulating the phase differences between the linearized optomechanical couplings, uni-directional state transmission can be achieved. The interface can function as an isolator, a circulator, and a two-way switch that routes the input states to a selected output channel. We show that…
Gradient-based optimal control of the non-Hermitian skin effect in optomechanical arrays
University of Ngaoundere（恩冈代雷大学）；Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University（斯坦伦布什大学高级研究所（STIAS），瓦伦伯格研究中心）；University of Bisha（比沙大学）；University of Business and Technology（商业与技术大学）；University of Maroua（马鲁阿大学）；University of Yaounde I（雅温得第一大学）
Mechanical resonators can act as excellent intermediaries to interface single photons in the microwave and optical domains due to their high quality factors. Nevertheless, the optical pump required to overcome the large energy difference between the frequencies can add significant noise to the transduced signal. Here we exploit the remarkable properties of thin-film gallium phosphide to demonstrate bi-directional on-chip conversion between microwave and optical frequencies, realized by piezoelectric actuation of a Gigahertz-frequency optomechanical resonator. The large optomechanical coupling …
The interaction between a high-frequency dilational mode of a thin dielectric film and an optical cavity field is studied theoretically in the membrane-in-the-middle setup. A derivation from first principles leads to a multi-mode optomechanical Hamiltonian where multiple cavity modes are coupled by the thickness variation of the membrane. For membrane thicknesses on the order of one micron, the frequency of this dilational mode is in the GHz range. This can be matched to the free spectral range of the optical cavity, such that the mechanical oscillator will resonantly couple cavity modes at di…
Directional transport is obtained in various multimode systems by driving multiple, nonreciprocally-interfering interactions between individual bosonic modes. However, systems sustaining the required number of modes become physically complex. In our microwave-optomechanical experiment, we show how to configure nonreciprocal transport between frequency components of a single superconducting cavity coupled to two drumhead oscillators. The frequency components are promoted to Floquet modes and generate the missing dimension to realize an isolator and a directional amplifier. A second cavity left …
We investigate optomechanical forces on a nearly lossless scatterer, such as an atom pumped far off-resonance or amicromirror, inside an optical ring cavity. Our model introduces two additional features to the cavity: an isolator is used to prevent circulation and resonant enhancement of the pump laser field and thus to avoid saturation of or damage to the scatterer, and an optical amplifier is used to enhance the effective $Q$-factor of the counterpropagating mode and thus to increase the velocity-dependent forces by amplifying the back-scattered light. We calculate friction forces, momentum …
We study the nonlinear optomechanically-induced transparency (OMIT) with gain and loss. We find that (i) for a single active cavity, significant enhancement can be achieved for the higher-order sidebands, including the transmission rate and the group delay; (ii) for active- passive-coupled cavities, hundreds of microsecond of optical delay or advance are attainable for the nonlinear sideband pulses in the parity-time-symmetric regime. The active higher-order OMIT effects, as firstly revealed here, open up the way to make a low-power optomechaical amplifier, which can amplify both the strength …
Wave mixing is an archetypical phenomenon in bosonic systems. In optomechanics, the bi-directional conversion between electromagnetic waves or photons at optical frequencies and elastic waves or phonons at radio frequencies is building on precisely this fundamental principle. Surface acoustic waves provide a versatile interconnect on a chip and, thus, enable the optomechanical control of remote systems. Here, we report on the coherent nonlinear three-wave mixing between the coherent fields of two radio frequency surface acoustic waves and optical laser photons via the dipole transition of a si…
