Quantum Optomechanics Research Articles

Two-timescale stochastic Langevin propagation for classical and quantum optomechanics

Interesting experimental signatures of quantum cavity optomechanics arise because the quantum back-action induces correlations between incident quantum shot noise and the cavity field. While the quantum linear theory of optomechanics (QLT) has provided vital understanding across many experimental platforms, in certain new set-ups it may be insufficient: analysis in the time domain may be needed, but QLT obtains only spectra in frequency space; and nonlinear behavior may be present. Direct solution of the stochastic equations of motion in time is an alternative, but unfortunately standard methods do not preserve the important optomechanical correlations. We introduce two-timescale stochastic Langevin (T2SL) propagation as an efficient and straightforward method to obtain time traces with the correct correlations. We show that T2SL, in contrast to standard stochastic simulations, can efficiently simulate correlation phenomena such as ponderomotive squeezing and reproduces accurately cavity sideband structures on the scale of the applied quantum noise and even complicated features entirely submerged below the quantum shot noise imprecision floor. We investigate nonlinear regimes and find where comparison is possible, that the method agrees with analytical results obtained with master equations at low temperatures and in perturbative regimes.

Near-field coupling of a levitated nanoparticle to a photonic crystal cavity

Quantum control of levitated dielectric particles is an emerging subject in quantum optomechanics. A major challenge is to efficiently measure and manipulate the particle's motion at the Heisenberg uncertainty limit. Here we present a nanophotonic interface suited to address this problem. By optically trapping a 150 nm silica particle and placing it in the near field of a photonic crystal cavity, we achieve tunable single-photon optomechanical coupling of up to $g_0/2\pi=9$ kHz, three orders of magnitude larger than previously reported for levitated cavity optomechanical systems. Efficient collection and guiding of light through the nanophotonic structure results in a per-photon displacement sensitivity that is increased by two orders of magnitude compared to conventional far-field detection. The demonstrated performance shows a promising route for room temperature quantum optomechanics.

Higher-Order Interactions in Quantum Optomechanics: Analysis of Quadratic Terms

This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second order operators which constitute an exactly closed commutators. We consider both types of standard position-field and the recently predicted non-standard momentum-field quadratic interactions, which is significant when the ratio of mechanical frequency to optical frequency is not negligible. This unexplored regime of large mechanical frequency can be investigated in few platforms including the superconducting electromechanics and simulating quantum cavity electrodynamic circuits. It has been shown that the existence of non-standard quadratic interaction could be observable under appropriate conditions.

Reaching the Limits of Enhancement in (Sub)Nanometer Metal Structures

Plasmonic enhancement has had remarkable success in optical coupling to the nanometer scale, enabling feats such as Raman spectroscopy with single molecule sensitivity. Here it is argued that much greater enhancements are possible in the near future by combining the gains of plasmonic resonances, directivity, subnanometer gaps, and permittivity near-zero materials. The pursuit of such extraordinary enhancements promises to bring new physics such as peering into the world of quantum optomechanics. It also promises new applications such as quantitative single molecule Raman spectroscopy and low photon number nonlinear optical switching. In addition, by pushing the limits of plasmonic enhancement, it is expected that the community will gain a greater appreciation of how physical phenomena such as nonlocality, surface scattering, and quantum tunneling each play a role in determining the ultimate performance.

Growing macroscopic superposition states via cavity quantum optomechanics

The investigation of macroscopic quantum phenomena is a current active area of research that offers significant promise to advance the forefronts of both fundamental and applied quantum science. Utilising the exquisite precision and control of quantum optics provides a powerful toolset for generating such quantum states where the types and ‘size’ of the states that can be generated are set by the experimental parameter regime available and the resourcefulness of the protocol applied. In this work we present a new multistep scheme to ‘grow’ macroscopic superposition states of motion of a mechanical oscillator via cavity quantum optomechanics. The scheme consists of a series of optical pulses interacting with a mechanical mode via radiation-pressure followed by photon-counting measurements. The multistep nature of our protocol allows macroscopic superposition states to be prepared with a relaxed requirement for the single-photon optomechanical coupling strength. To illustrate the experimental feasibility of our proposal, we quantify how initial mechanical thermal occupation and mechanical decoherence affects the non-classicality and macroscopicity of the states generated and show that our scheme is resilient to optical loss. The advantages of this protocol provide a promising path to grow non-classical mechanical quantum states to a macroscopic scale under realistic experimental conditions.

Tunable SNAP microresonators via internal ohmic heating

We demonstrate a thermally tunable surface nanoscale axial photonics (SNAP) platform. Stable tuning is achieved by heating a SNAP structure fabricated on the surface of a silica capillary with a metal wire positioned inside. Heating a SNAP microresonator with a uniform wire introduces uniform variation of its effective radius which results in constant shift of its resonance wavelengths. Heating with a nonuniform wire allows local nanoscale variation of the capillary effective radius, which enables differential tuning of the spectrum of SNAP structures, as well as the creation of temporary SNAP microresonators that exist only when current is applied. As an example, we fabricate two bottle microresonators coupled to each other and demonstrate differential tuning of their resonance wavelengths into and out of degeneracy with precision better than 0.2pm. The developed approach is beneficial for ultra-precise fabrication of tunable ultralow loss parity-time symmetric, optomechanical, and cavity quantum electrodynamics (QED) devices.

Exploring unresolved sideband, optomechanical strong coupling using a single atom coupled to a cavity

A major trend within the field of cavity QED is to boost the interaction strength between the cavity field and the atomic internal degrees of freedom of the trapped atom by decreasing the mode volume of the cavity. In such systems, it is natural to achieve strong atom-cavity coupling, where the coherent interaction strength exceeds the cavity linewidth, while the linewidth exceeds the atomic trap frequency. While most work focuses on coupling of photons to the internal degrees of freedom, additional rich dynamics can occur by considering the atomic motional degree of freedom as well. In particular, we show that such a system is a natural candidate to explore an interesting regime of quantum optomechanics, where the zero-point atomic motion yields a cavity frequency shift larger than its linewidth (so-called single-photon optomechanical strong coupling), but simultaneously where the motional frequency cannot be resolved by the cavity. We show that this regime can result in a number of remarkable phenomena, such as strong entanglement between the atomic wave function and the scattering properties of single incident photons, or an anomalous mechanism where the atomic motion can significantly heat up due to single-photon scattering, even if the atom is trapped tightly within the Lamb-Dicke limit.

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.

Not every dipole is the same: the hidden patterns of dipolar near fields

Nanophotonics is a fast-evolving scientific field studying light at the nanoscale. Its fascinating advances typically stem from concepts in modern physics, such as quantum optics, photonic crystals and optomechanics [1]. Occasionally, new insights appear even from the classical Maxwell’s equations of electromagnetism themselves [2].

Controllable photonic and phononic edge localization via optomechanically induced Kitaev phase.

Experimental realization of the Kitaev model is a greatly attractive topic due to the potential applications to build robust qubits against decoherence in topological quantum computation. In this work, we investigate the charged whispering-gallery microcavity array model and simulate the normal Kitaev chain under this mechanism in the first time. We find that the system reveals profound connections with the normal Kitaev chain and its some derivatives, and the topological property of the system depends on effective optomechanical coupling strength deeply. In optomechanically induced Kitaev topologically nontrivial phase, compared to the normal Kitaev chain in the Majorana basis, the novel and distinct structure of charged whispering-gallery microcavity array model leads to controllable photonic and phononic edge localization. Furthermore, we also simulate the extended Kitaev chain and show that two topologically different nontrivial phases of the system allow one to realize more freewheeling controllable photonic and phononic edge localization. Our model offers an alternative approach to correlate with other more complicated one-dimensional noninteracting spinless topological systems relevant to the p-wave superconducting pairing.

Dissipative versus dispersive coupling in quantum optomechanics: Squeezing ability and stability

Generation of squeezed light and optomechanical instability for dissipative type of opto- mechanical coupling is theoretically addressed for a cavity with the input mirror, serving as a mechanical oscillator, or an equivalent system. The problem is treated analytically for the case of resonance excitation or small detunings, mainly focusing on the bad cavity limit. A qualitative difference between the dissipative and purely dispersive coupling is reported. In particular, it is shown that, for the purely dissipative coupling in the bad cavity regime, the backaction is strongly reduced and the squeezing ability of the system is strongly suppressed, in contrast to the case of purely dispersive coupling. It is also shown that, for small detunings, stability diagrams for the cases of the purely dispersive and dissipative couplings are qualitatively identical to within the change of the sign of detuning. The results obtained are compared with those from the recent theoretical publications.

Generation of mechanical interference fringes by multi-photon counting

Exploring the quantum behaviour of macroscopic objects provides an intriguing avenue to study the foundations of physics and to develop a suite of quantum-enhanced technologies. One prominent path of study is provided by quantum optomechanics which utilizes the tools of quantum optics to control the motion of macroscopic mechanical resonators. Despite excellent recent progress, the preparation of mechanical quantum superposition states remains outstanding due to weak coupling and thermal decoherence. Here we present a novel optomechanical scheme that significantly relaxes these requirements allowing the preparation of quantum superposition states of motion of a mechanical resonator by exploiting the nonlinearity of multi-photon quantum measurements. Our method is capable of generating non-classical mechanical states without the need for strong single-photon coupling, is resilient against optical loss, and offers more favourable scaling against initial mechanical thermal occupation than existing schemes. Moreover, our approach allows the generation of larger superposition states by projecting the optical field onto NOON states. We experimentally demonstrate this multi-photon-counting technique on a mechanical thermal state in the classical limit and observe interference fringes in the mechanical position distribution that show phase super-resolution. This opens a feasible route to explore and exploit quantum phenomena at a macroscopic scale.

Injection locking of optomechanical oscillators via acoustic waves.

Injection locking is an effective technique for synchronization of oscillator networks and controlling the phase and frequency of individual oscillators. As such, exploring new mechanisms for injection locking of emerging oscillators is important for their usage in various systems. Here, we present the first demonstration of injection locking of a radiation pressure driven optomechanical oscillator (OMO) via acoustic waves. As opposed to previously reported techniques (based on pump modulation or direct application of a modulated electrostatic force), injection locking of OMO via acoustic waves does not require optical power modulation or physical contact with the OMO and it can be easily implemented on various platforms to lock different types of OMOs independent of their size and structure. Using this approach we have locked the phase and frequency of two distinct modes of a microtoroidal silica OMO to a piezoelectric transducer (PZT). We have characterized the behavior of the injection locked OMO with three acoustic excitation configurations and showed that even without proper acoustic impedance, matching the OMO can be locked to the PZT and tuned over 17 kHz with only -30 dBm of RF power fed to the PZT. The high efficiency, simplicity, and scalability of the proposed approach paves the road toward a new class of photonic systems that rely on synchronization of several OMOs to a single or multiple RF oscillators with applications in optical communication, metrology, and sensing. Beyond its practical applications, injection locking via acoustic waves can be used in fundamental studies in quantum optomechanics where thermal and optical isolation of the OMO are critical.

Reshaping the phonon energy landscape of nanocrystals inside a terahertz plasmonic nanocavity

Phonons (quanta of collective vibrations) are a major source of energy dissipation and drive some of the most relevant properties of materials. In nanotechnology, phonons severely affect light emission and charge transport of nanodevices. While the phonon response is conventionally considered an inherent property of a nanomaterial, here we show that the dipole-active phonon resonance of semiconducting (CdS) nanocrystals can be drastically reshaped inside a terahertz plasmonic nanocavity, via the phonon strong coupling with the cavity vacuum electric field. Such quantum zero-point field can indeed reach extreme values in a plasmonic nanocavity, thanks to a mode volume well below λ3/107. Through Raman measurements, we find that the nanocrystals within a nanocavity exhibit two new “hybridized” phonon peaks, whose spectral separation increases with the number of nanocrystals. Our findings open exciting perspectives for engineering the optical phonon response of functional nanomaterials and for implementing a novel platform for nanoscale quantum optomechanics.

Higher-Order Interactions in Quantum Optomechanics: Analytical Solution of Nonlinearity

A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While, the zeroth order linearization approximation to the operators is normally used, here first and second order truncation perturbation schemes are proposed. These schemes employ higher-order system operators, and then approximate number operators with their corresponding mean boson numbers, only where needed. Spectral densities of higher-order operators are derived, and an expression for the second-order correlation function at zero time-delay has been found, which reveals that the cavity photon occupation of an ideal laser at threshold reaches $\sqrt{6}-2$, in good agreement with extensive numerical calculations. As further applications, analysis of the quantum anharmonic oscillator, calculation of $Q-$functions, analysis of quantum limited amplifiers, and nondemoliton measurements.

Building mechanical Greenberger-Horne-Zeilinger and cluster states by harnessing optomechanical quantum steerable correlations

Greenberger-Horne-Zeilinger (GHZ) and cluster states are two typical kinds of multipartite entangled states and can respectively be used for realizing quantum networks and one-way computation. We propose a feasible scheme for generating Gaussian GHZ and cluster states of multiple mechanical oscillators by pulsed cavity optomechanics. In our scheme, each optomechanical cavity is driven by a blue-detuned pulse to establish quantum steerable correlations between the cavity output field and the mechanical oscillator, and the cavity outputs are combined at a beam-splitter array with given transmissivity and reflectivity for each beam splitter. We show that by harnessing the light-mechanical steerable correlations, the mechanical GHZ and cluster states can be realized via homodyne detection on the amplitude and phase quadratures of the output fields from the beam-splitter array. These achieved mechanical entangled states can be viewed as the output states of an effective mechanical beam-splitter array with the mechanical inputs prepared in squeezed states with the light-mechanical steering. The effects of detection efficiency and thermal noise on the achieved mechanical states are investigated. The present scheme does not require externally injected squeezing and it can also be applicable to other systems such as light-atomic-ensemble interface, apart from optomechanical systems.

The influence of thermal photons on the dynamics of a quantum optomechanics system with quadratic cavity–membrane couplings

In this paper we investigate the influence of thermal photons as an inevitable source of damping on the dynamics of a quantum optomechanics system consisting of a suspended membrane in an optical cavity. The membrane is putted inside the cavity, in such a way that it plays the role of a movable mirror for each subcavity. In this respect, we investigate about the tunnelling of the photons between the two subcavities as well as the dynamics of membrane position in the mean-field approximation. In particular, the influences of thermal photons (in the presence of ”photon” and ”phonon” loss rates) on the time evolution of the above-mentioned quantities are evaluated and studied through which it is observed that the thermal photons considerably affects on the population inversion of photons number whenever the square coupling constant of cavity–membrane is weak. Inversely, the influence of thermal photons on the position of membrane is more visible for strong square coupling. Furthermore, it is demonstrated that generally the discussed properties can be appropriately adjusted by tuning the involved damping parameters.

Optomechanical properties of GaAs/AlAs micropillar resonators operating in the 18 GHz range.

Recent experiments demonstrated that GaAs/AlAs based micropillar cavities are promising systems for quantum optomechanics, allowing the simultaneous three-dimensional confinement of near-infrared photons and acoustic phonons in the 18-100 GHz range. Here, we investigate through numerical simulations the optomechanical properties of this new platform. We evidence how the Poisson's ratio and semiconductor/vacuum boundary conditions lead to very distinct features in the mechanical and optical three-dimensional confinement. We find a strong dependence of the mechanical quality factor and strain distribution on the micropillar radius, in great contrast to what is predicted and observed in the optical domain. The derived optomechanical coupling constants g0 reach ultra-large values in the 106 rad/s range.

Quantum Correlations of Light from a Room-Temperature Mechanical Oscillator

The coupling of laser light to a mechanical oscillator via radiation pressure leads to the emergence of quantum mechanical correlations between the amplitude and phase quadrature of the laser beam. These correlations form a generic non-classical resource which can be employed for quantum-enhanced force metrology, and give rise to ponderomotive squeezing in the limit of strong correlations. To date, this resource has only been observed in a handful of cryogenic cavity optomechanical experiments. Here, we demonstrate the ability to efficiently resolve optomechanical quantum correlations imprinted on an optical laser field interacting with a room temperature nanomechanical oscillator. Direct measurement of the optical field in a detuned homodyne detector ("variational measurement") at frequencies far from the resonance frequency of the oscillator reveal quantum correlations at the few percent level. We demonstrate how the absolute visibility of these correlations can be used for a quantum-enhanced estimation of the quantum back-action force acting on the oscillator, and provides for an enhancement in the relative signal-to-noise ratio for the estimation of an off-resonant external force, even at room temperature.

Effect of oxygen plasma on nanomechanical silicon nitride resonators

Precise control of tensile stress and intrinsic damping is crucial for the optimal design of nanomechanical systems for sensor applications and quantum optomechanics in particular. In this letter, we study the influence of oxygen plasma on the tensile stress and intrinsic damping of nanomechanical silicon nitride resonators. Oxygen plasma treatments are common steps in micro and nanofabrication. We show that oxygen plasma for only a few minutes oxidizes the silicon nitride surface, creating several nanometer thick silicon dioxide layers with a compressive stress of 1.30(16) GPa. Such oxide layers can cause a reduction in the effective tensile stress of a 50 nm thick stoichiometric silicon nitride membrane by almost 50%. Additionally, intrinsic damping linearly increases with the silicon dioxide film thickness. An oxide layer of 1.5 nm grown in just 10 s in a 50 W oxygen plasma almost doubled the intrinsic damping. The oxide surface layer can be efficiently removed in buffered hydrofluoric acid.