Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the 3 dB Limit

Optomechanical squeezing with strong harmonic mechanical driving

In this paper, we propose an optomechanical scheme for generating mechanical squeezing over the 3 dB limit, with the mechanical mirror being driven by a strong and linear harmonic force. In contrast to parametric mechanical driving, the linearly driven force shakes the mechanical mirror periodically oscillating at twice the mechanical eigenfrequency with large amplitude, where the mechanical mirror can be dissipatively stabilized by the engineered cavity reservoir to a dynamical squeezed steady state with a maximum degree of squeezing over 8 dB. The mechanical squeezing of more than 3 dB can be achieved even for a mechanical thermal temperature larger than 100 mK. The scheme can be implemented in a cascaded optomechanical setup, with potential applications in engineering continuous variable entanglement and quantum sensing.

Nonreciprocal strong mechanical squeezing based on the Sagnac effect and two-tone driving

We propose a scheme for generating nonreciprocal strong mechanical squeezing by using two-tone lasers to drive a spinning optomechanical system. For given driving frequencies, strong mechanical squeezing of the breathing mode in the spinning resonator can be achieved in a chosen driving direction but not in the other. The nonreciprocity originates from the Sagnac effect caused by the resonator's spinning. We also find the classical nonreciprocity and the quantum nonreciprocity can be switched by simply changing the angular velocity of the spinning resonator. We show that the scheme is robust to the system's dissipations and the mechanical thermal noise. This work may be meaningful for the study of nonreciprocal device and quantum precision measurement.

Spatial susceptibility modulation and controlled unidirectional reflection amplification via four-wave mixing

Control of unidirectional light propagation is of paramount importantance to optical signal processing and optical communication. Especially, the amplified optical signal can isolate noise well that may provide more applications. In this work, we propose a dynamically modulated regime to realize unidirectional reflection amplification in a short and dense uniform atomic medium, and all atoms are driven into four-level double-Λ type by two coupling fields with linearly varied intensities along x direction and two weak probe fields. Based on four-wave mixing resonance and the broken spatial symmetry, the complete nonreciprocal reflection (unidirectional reflection) can be amplified with reflectivity more than 2.0, even to 6.0. In addition, the width, height, and position of the unidirectional reflection bands can be tunable. Thus, our regime is feasible and may inspire further applications in all-optical networks that require controllable unidirectional light amplification.

Mechanical squeezing in an active-passive-coupled double-cavity optomechanical system via pump modulation

We focus on the generation of mechanical squeezing by using periodically amplitude-modulated laser to drive an active-passive-coupled double-cavity optomechanical system, where the coupled gain cavity and loss cavity can form into a parity-time (P T)-symmetry system. The numerical analysis of the system stability shows that the system is more likely to be stable in the unbroken-P T-symmetry regime than in the broken-P T-symmetry regime. The mechanical squeezing in the active-passive system exhibits stronger robustness against the thermal noise than that in the passive-passive system, and the so-called 3 dB limit can be broken in the resolved-sideband regime. Furthermore, it is also found that the mechanical squeezing obtained in the unbroken-P T-symmetry region is stronger than that in the broken-P T-symmetry region. This work may be meaningful for the quantum state engineering in the gain-loss quantum system that contributes to the study of P T-symmetric physics in the quantum regime.

High-precision multiparameter estimation of mechanical force by quantum optomechanics

A nanomechanical oscillator can be used as a sensitive probe of a small linearized mechanical force. We propose a simple quantum optomechanical scheme using a coherent light mode in the cavity and weak short-pulsed light-matter interactions. Our main result is that if we transfer some displacement to the mechanical mode in an initialization phase, then a much weaker optomechanical interaction is enough to obtain a high-precision multiparameter estimation of the unknown force. This approach includes not only estimating the displacement caused by the force but also simultaneously observing the phase shift and squeezing of the mechanical mode. We show that the proposed scheme is robust against typical experimental imperfections and demonstrate the feasibility of our scheme using orders of magnitude weaker optomechanical interactions than in previous related works. Thus, we present a simple, robust estimation scheme requiring only very weak light-matter interactions, which could open the way to new nanomechanical sensors.

Beating the 3 dB Limit for Intracavity Squeezing and Its Application to Nondemolition Qubit Readout

While the squeezing of a propagating field can, in principle, be made arbitrarily strong, the cavity-field squeezing is subject to the well-known 3 dB limit, and thus has limited applications. Here, we propose the use of a fully quantum degenerate parametric amplifier (DPA) to beat this squeezing limit. Specifically, we show that by simply applying a two-tone driving to the signal mode, the pump mode can, counterintuitively, be driven by the photon loss of the signal mode into a squeezed steady state with, in principle, an arbitrarily high degree of squeezing. Furthermore, we demonstrate that this intracavity squeezing can increase the signal-to-noise ratio of longitudinal qubit readout exponentially with the degree of squeezing. Correspondingly, an improvement of the measurement error by many orders of magnitude can be achieved even for modest parameters. In stark contrast, using intracavity squeezing of the semiclassical DPA cannot practically increase the signal-to-noise ratio and thus improve the measurement error. Our results extend the range of applications of DPAs and open up new opportunities for modern quantum technologies.

Mechanical Squeezing via Unstable Dynamics in a Microcavity

We theoretically show that strong mechanical quantum squeezing in a linear optomechanical system can be rapidly generated through the dynamical instability reached in the far red-detuned and ultrastrong coupling regime. We show that this mechanism, which harnesses unstable multimode quantum dynamics, is particularly suited to levitated optomechanics, and we argue for its feasibility for the case of a levitated nanoparticle coupled to a microcavity via coherent scattering. We predict that for submillimeter-sized cavities the particle motion, initially thermal and well above its ground state, becomes mechanically squeezed by tens of decibels on a microsecond timescale. Our results bring forth optical microcavities in the unresolved sideband regime as powerful mechanical squeezers for levitated nanoparticles, and hence as key tools for quantum-enhanced inertial and force sensing.

Improving few-photon optomechanical effects with coherent feedback

Few-photon effects such as photon blockade and tunneling have potential applications in modern quantum technology. To enhance the few-photon effects in an optomechanical system, we introduce a coherent feedback loop to cavity mode theoretically. By studying the second-order correlation function, we show that the photon blockade effect can be improved with feedback. Under appropriate parameters, the photon blockade effect exists even when cavity decay rate is larger than the single-photon optomechanical coupling coefficient, which may reduce the difficulty of realizing single-photon source in experiments. Through further study of the third-order correlation function, we show that the tunneling effect can also be enhanced by feedback. In addition, we discuss the application of feedback on Schrödinger-cat state generation in an optomechanical system. The result shows that the fidelity of cat state generation can be improved in the presence of feedback loop.

Quantum mechanics-free subsystem with mechanical oscillators

Quantum mechanics sets a limit for the precision of continuous measurement of the position of an oscillator. We show how it is possible to measure an oscillator without quantum back-action of the measurement by constructing one effective oscillator from two physical oscillators. We realize such a quantum mechanics-free subsystem using two micromechanical oscillators, and show the measurements of two collective quadratures while evading the quantum back-action by 8 decibels on both of them, obtaining a total noise within a factor of 2 of the full quantum limit. This facilitates the detection of weak forces and the generation and measurement of nonclassical motional states of the oscillators. Moreover, we directly verify the quantum entanglement of the two oscillators by measuring the Duan quantity 1.4 decibels below the separability bound.

Large and robust mechanical squeezing of optomechanical systems in a highly unresolved sideband regime via Duffing nonlinearity and intracavity squeezed light

We propose a scheme to generate strong and robust mechanical squeezing in an optomechanical system in the highly unresolved sideband (HURSB) regime with the help of the Duffing nonlinearity and intracavity squeezed light. The system is formed by a standard optomechanical system with the Duffing nonlinearity (mechanical nonlinearity) and a second-order nonlinear medium (optical nonlinearity). In the resolved sideband regime, the second-order nonlinear medium may play a destructive role in the generation of mechanical squeezing. However, it can significantly increase the mechanical squeezing (larger than 3dB) in the HURSB regime when the parameters are chosen appropriately. Finally, we show the mechanical squeezing is robust against the thermal fluctuations of the mechanical resonator. The generation of large and robust mechanical squeezing in the HURSB regime is a combined effect of the mechanical and optical nonlinearities.

Laser Cooling of a Nanomechanical Oscillator to Its Zero-Point Energy

Optomechanical systems in the well-resolved-sideband regime are ideal for studying a myriad of quantum phenomena with mechanical systems, including backaction-evading measurements, mechanical squeezing, and nonclassical states generation. For these experiments, the mechanical oscillator should be prepared in its ground state, i.e., exhibit negligible residual excess motion compared to its zero-point motion. This can be achieved using the radiation pressure of laser light in the cavity by selectively driving the lower motional sideband, leading to sideband cooling. To date, the preparation of sideband-resolved optical systems to their zero-point energy has eluded laser cooling because of strong optical absorption heating. The alternative method of passive cooling suffers from the same problem, as the requisite milliKelvin environment is incompatible with the strong optical driving needed by many quantum protocols. Here, we employ a highly sideband-resolved silicon optomechanical crystal in a ^{3}He buffer-gas environment at ∼2  K to demonstrate laser sideband cooling to a mean thermal phonon occupancy of 0.09_{-0.01}^{+0.02} quantum (self-calibrated using motional sideband asymmetry), which is -7.4  dB of the oscillator's zero-point energy and corresponds to 92% ground state probability. Achieving such low occupancy by laser cooling opens the door to a wide range of quantum-optomechanical experiments in the optical domain.

Large mechanical squeezing beyond 3dB of hybrid atom-optomechanical systems in a highly unresolved sideband regime

We propose a scheme for the generation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in the highly unresolved sideband (HURSB) regime where the decay rate of cavity is much larger than the frequency of the mechanical oscillator. The system is formed by two two-level atomic ensembles and an optomechanical system with cavity driven by two lasers with different amplitudes. In the HURSB regime, the squeezing of the movable mirror can not be larger than 3dB if no atomic ensemble or only one atomic ensemble is put into the optomechanical system. However, if two atomic ensembles are put into the optomechanical system, the strong mechanical squeezing beyond 3dB is achieved even in the HURSB regime. Our scheme paves the way toward the implementation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in experiments.

Quantum Signature of a Squeezed Mechanical Oscillator

Recent optomechanical experiments have observed nonclassical properties in macroscopic mechanical oscillators. A key indicator of such properties is the asymmetry in the strength of the motional sidebands produced in the probe electromagnetic field, which is originated by the noncommutativity between the oscillator ladder operators. Here we extend the analysis to a squeezed state of an oscillator embedded in an optical cavity, produced by the parametric effect originated by a suitable combination of optical fields. The motional sidebands assume a peculiar shape, related to the modified system dynamics, with asymmetric features revealing and quantifying the quantum component of the squeezed oscillator motion.

Measurement of Motion beyond the Quantum Limit by Transient Amplification

Through simultaneous but unequal electromechanical amplification and cooling processes, we create a method for a nearly noiseless pulsed measurement of mechanical motion. We use transient electromechanical amplification (TEA) to monitor a single motional quadrature with a total added noise -8.5±2.0  dB relative to the zero-point motion of the oscillator, or equivalently the quantum limit for simultaneous measurement of both mechanical quadratures. We demonstrate that TEA can be used to resolve fine structure in the phase space of a mechanical oscillator by tomographically reconstructing the density matrix of a squeezed state of motion. Without any inference or subtraction of noise, we directly observe a squeezed variance 2.8±0.3  dB below the oscillator's zero-point motion.

Optical backaction-evading measurement of a mechanical oscillator

Quantum mechanics imposes a limit on the precision of a continuous position measurement of a harmonic oscillator, due to backaction arising from quantum fluctuations in the measurement field. This standard quantum limit can be surpassed by monitoring only one of the two non-commuting quadratures of the motion, known as backaction-evading measurement. This technique has not been implemented using optical interferometers to date. Here we demonstrate, in a cavity optomechanical system operating in the optical domain, a continuous two-tone backaction-evading measurement of a localized gigahertz-frequency mechanical mode of a photonic-crystal nanobeam cryogenically and optomechanically cooled close to the ground state. Employing quantum-limited optical heterodyne detection, we explicitly show the transition from conventional to backaction-evading measurement. We observe up to 0.67 dB (14%) reduction of total measurement noise, thereby demonstrating the viability of backaction-evading measurements in nanomechanical resonators for optical ultrasensitive measurements of motion and force.

Measurements of motion that avoid quantum backaction, with the potential to surpass the standard quantum limit, have so far been demonstrated using microwave radiation. Here, Shomroni, Qiu et al. demonstrate a backaction-evading measurement of the motion of a nanomechanical beam using laser light.

Method of Higher-order Operators for Quantum Optomechanics

We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings. Similarly, a higher-order resonance shift exists appearing as changes in both of the optical and mechanical resonances. We provide the first known method to explicitly estimate the population of coherent phonons. We also calculate corrections to spring effect due to higher-order interactions and coherent phonons, and show that these corrections can be quite significant in measurement of single-photon optomechanical interaction rate. It is shown that there exists non-unique and various choices for the higher-order operators to solve the optomechanical interaction with different multiplicative noise terms, among which a minimal basis offers exactly linear Langevin equations, while decoupling one Langevin equation and thus leaving the whole standard optomechanical problem exactly solvable by explicit expressions. We finally present a detailed treatment of multiplicative noise as well as nonlinear dynamic stability phases by the method of higher-order operators. Similar approach can be used outside the domain of standard optomechanics to quadratic and all other types of nonlinear interactions in quantum physics.

Strong mechanical squeezing in an electromechanical system

The mechanical squeezing can be used to explore quantum behavior in macroscopic system and realize precision measurement. Here we present a potentially practical method for generating strong squeezing of the mechanical oscillator in an electromechanical system. Through the Coulomb interaction between a charged mechanical oscillator and two fixed charged bodies, we engineer a quadratic electromechanical Hamiltonian for the vibration mode of mechanical oscillator. We show that the strong position squeezing would be obtained on the currently available experimental technologies.

Quantum-Limited Directional Amplifiers with Optomechanics

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; we discuss how this noise can be suppressed, a crucial aspect for technological applications. The isolation bandwidth in both is of the order of the mechanical linewidth divided by the amplitude gain. We derive the bandwidth and gain-bandwidth product for both and find that the phase-sensitive amplifier has an unlimited gain-bandwidth product. Our study represents an important step toward flexible, on-chip integrated nonreciprocal amplifiers of microwave signals.