Quantum measurement of phonon shot noise

Enhanced nonlinear optomechanics in a coupled-mode photonic crystal device

The nonlinear component of the optomechanical interaction between light and mechanical vibration promises many exciting classical and quantum mechanical applications, but is generally weak. Here we demonstrate enhancement of nonlinear optomechanical measurement of mechanical motion by using pairs of coupled optical and mechanical modes in a photonic crystal device. In the same device we show linear optomechanical measurement with a strongly reduced input power and reveal how both enhancements are related. Our design exploits anisotropic mechanical elasticity to create strong coupling between mechanical modes while not changing optical properties. Additional thermo-optic tuning of the optical modes is performed with an auxiliary laser and a thermally-optimised device design. We envision broad use of this enhancement scheme in multimode phonon lasing, two-phonon heralding and eventually nonlinear quantum optomechanics.

Asymmetry-Based Quantum Backaction Suppression in Quadratic Optomechanics

As the field of optomechanics advances, quadratic dispersive coupling (QDC) represents an increasingly feasible path toward qualitatively new functionality. However, the leading QDC geometries generate linear dissipative coupling and an associated quantum radiation force noise that is detrimental to QDC applications. Here, we propose a simple geometry that dramatically reduces this noise without altering the QDC strength. We identify optimal regimes of operation, and discuss advantages within the examples of optical levitation and nondestructive phonon measurement.

Quantum Spectrometry for Arbitrary Noise

We present a technique for recovering the spectrum of a non-Markovian bosonic bath and/or non-Markovian noises coupled to a harmonic oscillator. The treatment is valid under the conditions that the environment is large and hot compared to the oscillator, and that its temporal autocorrelation functions are symmetric with respect to time translation and reflection-criteria which we consider fairly minimal. We model a demonstration of the technique as deployed in the experimental scenario of a nanosphere levitated in a Paul trap, and show that it would effectively probe the spectrum of an electric field noise source from 10^{2} to 10^{6}  Hz with a resolution inversely proportional to the measurement time. This technique may be deployed in quantum sensing, metrology, computing, and in experimental probes of foundational questions.

Ground-state cooling of mechanical oscillator via quadratic optomechanical coupling with two coupled optical cavities

We present a scheme for the electromagnetically induced transparency (EIT)-like nonlinear ground-state cooling in a double-cavity optomechanical system in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator, an additional auxiliary cavity is coupled to the optomechanical cavity. The optimum cooling conditions is derived, based on which the heating process can be well suppressed and the mechanical resonator can be cooled with an optimal effect to near its ground state through EIT-like cooling mechanism even in unresolved sideband regime. It is demonstrated by numerical simulations that not only the average phonon number of steady state is lower than that of single-cavity optomechanical system, but also the cooling rate is greatly faster than that of the linear optomechanical coupling due to the two-phonon cooling process in the quadratic coupling. Also, the ground-state cooling is achievable even with a relatively weak quadratic coupling strengthby tunning the coupling between two cavities to reach the optimum cooling conditions, thus provides an solution for overcoming the limitations of weak quadratic coupling rate in experiments. The proposed approach provides a platform for quantum manipulation of macroscopic mechanical devices beyond the resolved sideband limit and linear coupling regime.

Certifying Nonclassical Behavior for Negative Keldysh Quasiprobabilities

We introduce an experimental test for ruling out classical explanations for the statistics obtained when measuring arbitrary observables at arbitrary times using individual detectors. This test requires some trust in the measurements, represented by a few natural assumptions on the detectors. In quantum theory, the considered scenarios are well captured by von Neumann measurements. These can be described naturally in terms of the Keldysh quasiprobability distribution (KQPD), and the imprecision and backaction exerted by the measurement apparatus. We find that classical descriptions can be ruled out from measured data if and only if the KQPD exhibits negative values. We provide examples based on simulated data, considering the influence of a finite amount of statistics. In addition to providing an experimental tool for certifying nonclassicality, our results bestow an operational meaning upon the nonclassical nature of negative quasiprobability distributions such as the Wigner function and the full counting statistics.

Nonlinear cavity optomechanics with nanomechanical thermal fluctuations

Although the interaction between light and motion in cavity optomechanical systems is inherently nonlinear, experimental demonstrations to date have allowed a linearized description in all except highly driven cases. Here, we demonstrate a nanoscale optomechanical system in which the interaction between light and motion is so large (single-photon cooperativity C0≈103) that thermal motion induces optical frequency fluctuations larger than the intrinsic optical linewidth. The system thereby operates in a fully nonlinear regime, which pronouncedly impacts the optical response, displacement measurement and radiation pressure backaction. Specifically, we measure an apparent optical linewidth that is dominated by thermo-mechanically induced frequency fluctuations over a wide temperature range, and show that in this regime thermal displacement measurements cannot be described by conventional analytical models. We perform a proof-of-concept demonstration of exploiting the nonlinearity to conduct sensitive quadratic readout of nanomechanical displacement. Finally, we explore how backaction in this regime affects the mechanical fluctuation spectra.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Design of a quasi-2D photonic crystal optomechanical cavity with tunable, large x2-coupling

We present the optical and mechanical design of a mechanically compliant quasi-two-dimensional photonic crystal cavity formed from thin-film silicon in which a pair of linear nanoscale slots are used to create two coupled high-Q optical resonances. The optical cavity supermodes, whose frequencies are designed to lie in the 1500 nm wavelength band, are shown to interact strongly with mechanical resonances of the structure whose frequencies range from a few MHz to a few GHz. Depending upon the symmetry of the mechanical modes and the symmetry of the slot sizes, we show that the optomechanical coupling between the optical supermodes can be either linear or quadratic in the mechanical displacement amplitude. Tuning of the nanoscale slot size is also shown to adjust the magnitude and sign of the cavity supermode splitting 2J, enabling near-resonant motional scattering between the two optical supermodes and greatly enhancing the x²-coupling strength. Specifically, for the fundamental flexural mode of the central nanobeam of the structure at 10 MHz the per-phonon linear cross-mode coupling rate is calculated to be g˜_+-/2π=1MHz, corresponding to a per-phonon x²-coupling rate of g˜^'/2π=1kHz for a mode splitting 2J/2π = 1 GHz which is greater than the radiation-limited supermode linewidths.

Negative Full Counting Statistics Arise from Interference Effects

The Keldysh-ordered full counting statistics is a quasiprobability distribution describing the fluctuations of a time-integrated quantum observable. While it is well known that this distribution can fail to be positive, the interpretation and origin of this negativity has been somewhat unclear. Here, we show how the full counting statistics can be tied to trajectories through Hilbert space, and how this directly connects negative quasiprobabilities to an unusual interference effect. Our findings are illustrated with the example of energy fluctuations in a driven bosonic resonator; we discuss how negative quasiprobability here could be detected experimentally using superconducting microwave circuits.

Interplay of driving and frequency noise in the spectra of vibrational systems

We study the spectral effect of the fluctuations of the vibration frequency. Such fluctuations play a major role in nanomechanical and other mesoscopic vibrational systems. We find that, for periodically driven systems, the interplay of the driving and frequency fluctuations results in specific spectral features. We present measurements on a carbon nanotube resonator and show that our theory allows not only the characterization of the frequency fluctuations but also the quantification of the decay rate without ring-down measurements. The results bear on identifying the decoherence of mesoscopic oscillators and on the general problem of resonance fluorescence and light scattering by oscillators.

Exchange fluctuation theorem for heat transport between multiterminal harmonic systems

We study full counting statistics for transferred heat and entropy production between multiterminal systems in absence of a finite junction. The systems are modeled as collections of coupled harmonic oscillators, which are kept at different equilibrium temperatures and are connected via arbitrary time-dependent couplings. Following consistent quantum framework and two-time measurement concept we obtain analytical expressions for the generalized cumulant generating function. We discuss transient and steady-state fluctuation theorems for the transferred quantities. We also address the effect of coupling strength on the exchange fluctuation theorem.

Sharp tunneling peaks in a parametric oscillator: quantum resonances missing in the rotating wave approximation

We describe a new mechanism of tunneling between period-two vibrational states of a weakly nonlinear, parametrically modulated oscillator. The tunneling results from resonant transitions induced by the fast oscillating terms conventionally disregarded in the rotating wave approximation (RWA). The tunneling amplitude displays resonant peaks as a function of the modulation frequency; near the maxima it is exponentially larger than the RWA tunneling amplitude.

Full-counting statistics of heat transport in harmonic junctions: transient, steady states, and fluctuation theorems

We study the statistics of heat transferred in a given time interval t_{M}, through a finite harmonic chain, called the center, which is connected to two heat baths, the left (L) and the right (R), that are maintained at two temperatures. The center atoms are driven by external time-dependent forces. We calculate the cumulant generating function (CGF) for the heat transferred out of the left lead, Q_{L}, based on the two-time quantum measurement concept and using the nonequilibrium Green's function method. The CGF can be concisely expressed in terms of Green's functions of the center and an argument-shifted self-energy of the lead. The expression of the CGF is valid in both transient and steady-state regimes. We consider three initial conditions for the density operator and show numerically, for a one-atom junction, how their transient behaviors differ from each other but, finally, approach the same steady state, independent of the initial distributions. We also derive the CGF for the joint probability distribution P(Q_{L},Q_{R}), and discuss the correlations between Q_{L} and Q_{R}. We calculate the CGF for total entropy production in the reservoirs. In the steady state we explicitly show that the CGFs obey steady-state fluctuation theorems. We obtain classical results by taking ℏ→0. We also apply our method to the counting of the electron number and electron energy, for which the associated self-energy is obtained from the usual lead self-energy by multiplying a phase and shifting the contour time, respectively.

Continuous quantum hypothesis testing

I propose a general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations. For example, the hypotheses can be about the presence of a weak classical signal continuously coupled to a quantum sensor, or about competing quantum or classical models of the dynamics of a system. This generalization makes the theory useful for quantum detection and experimental tests of quantum mechanics in general. In the case of continuous measurements, the theory is significantly simplified to produce compact formulas for the likelihood ratio, the central quantity in statistical hypothesis testing. The likelihood ratio can then be computed efficiently in many cases of interest. Two potential applications of the theory, namely, quantum detection of a classical stochastic waveform and test of harmonic-oscillator energy quantization, are discussed.

Optomechanical cavity cooling of an atomic ensemble

We demonstrate cavity sideband cooling of a single collective motional mode of an atomic ensemble down to a mean phonon occupation number ⟨n⟩(min⁡)=2.0(-0.3)(+0.9). Both ⟨n⟩(min) and the observed cooling rate are in good agreement with an optomechanical model. The cooling rate constant is proportional to the total photon scattering rate by the ensemble, demonstrating the cooperative character of the light-emission-induced cooling process. We deduce fundamental limits to cavity cooling either the collective mode or, sympathetically, the single-atom degrees of freedom.

Optomechanical trampoline resonators

We report on the development of optomechanical "trampoline" resonators composed of a tiny SiO(2)/Ta(2)O(5) dielectric mirror on a silicon nitride micro-resonator. We observe optical finesses of up to 4 × 10(4) and mechanical quality factors as high as 9 × 10(5) in relatively massive (~100 ng) and low frequency (10-200 kHz) devices. This results in a photon-phonon coupling efficiency considerably higher than previous Fabry-Perot-type optomechanical systems. These devices are well suited to ultra-sensitive force detection, ground-state optical cooling experiments, and demonstrations of quantum dynamics for such systems.

Unified description of charge transfer mechanisms and vibronic dynamics in nanoscale junctions

We propose a general framework that unifies the description of counting statistics of transmitted (fermionic) charges as it is commonly used in the quantum transport community with the description of counting statistics of phonons (bosons). As a particular example, we study on the same footing the counting statistics of electrons transferred through a molecular junction and the corresponding population dynamics of the associated molecular vibrational mode. In the tunnel limit, non-perturbative results in the electron-phonon interaction are derived that unify complementary approaches based on rate equations or on the use of non-equilibrium Green functions.

Spectrum of an oscillator with jumping frequency and the interference of partial susceptibilities

We study an underdamped oscillator with random frequency jumps. We describe the oscillator spectrum in terms of coupled susceptibilities for different-frequency states. Depending on the parameters, the spectrum has a fine structure or displays a single asymmetric peak. For nanomechanical resonators with a fluctuating number of attached molecules, it is found in a simple analytical form. The results bear on dephasing in various types of systems with jumping frequency.

Tunable cavity optomechanics with ultracold atoms

We present an atom-chip-based realization of quantum cavity optomechanics with cold atoms localized within a Fabry-Perot cavity. Effective subwavelength positioning of the atomic ensemble allows for tuning the linear and quadratic optomechanical coupling parameters, varying the sensitivity to the displacement and strain of a compressible gaseous medium. We observe effects of such tuning on cavity optical nonlinearity and optomechanical frequency shifts, providing their first characterization in the quadratic-coupling regime.