A general theory is presented to describe optomechanical interactions of acoustic phonons, having extremely long lifetimes in superfluid $^4$He, with optical photons in the medium placed in a suitable electromagnetic cavity. The acoustic nonlinearity in the fluid motion is included to consider processes beyond the usual linear process involving absorption or emission of one phonon at a time. We first apply our formulation to the simplest one-phonon process involving the usual resonant anti-Stokes upconversion of an incident optical mode. However, when the allowed optical cavity modes are such that there is no single-phonon mode in the superfluid which can give rise to a resonant allowed anti-Stokes mode, we must consider the possibility of two phonon upconversion. For such a case, we show that the two step two phonon process could be dominant. We present arguments for large two step process and negligible single step two phonon contribution. The two step process also shows interesting quantum interference among different transition pathways.
Excitations in superfluid helium represent attractive mechanical degrees of freedom for cavity optomechanics schemes. Here we numerically and analytically investigate the properties of optomechanical resonators formed by thin films of superfluid $^4$He covering micrometer-scale whispering gallery mode cavities. We predict that through proper optimization of the interaction between film and optical field, large optomechanical coupling rates $g_0>2π\times 100$ kHz and single photon cooperativities $C_0>10$ are achievable. Our analytical model reveals the unconventional behaviour of these thin fi…
Optomechanical systems couple an electromagnetic cavity to a mechanical resonator which is typically formed from a solid object. The range of phenomena accessible to these systems depends on the properties of the mechanical resonator and on the manner in which it couples to the cavity fields. In both respects, a mechanical resonator formed from superfluid liquid helium offers several appealing features: low electromagnetic absorption, high thermal conductivity, vanishing viscosity, well-understood mechanical loss, and in situ alignment with cryogenic cavities. In addition, it offers degrees of…
We theoretically investigate the optomechanically induced transparency (OMIT) phenomenon in a N-cavity optomechanical system doped with a pair of Rydberg atoms with the presence of a strong pump field and a weak probe field applied to the Nth cavity. 2N-1(N<10) number OMIT windows can be observed in the output field when N cavities coupled with N mechanical oscillators, respectively. But, the mechanical oscillators coupled with different even-odd label cavities lead to different effect on OMIT. On the other hand, two additional transparent windows (extra resonances) are presented, if two Rydbe…
We consider an optomechanical system that is composed of a mechanical and an optical mode interacting through a linear and quadratic optomechanical dispersive couplings. The system is operated in an unresolved side band limit with a high quality factor mechanical resonator. Such a system then acts as parametrically driven oscillator, giving access to an intensity assisted tunability of the spring constant. This enables the operation of optomechanical system in its 'soft mode' wherein the mechanical spring softens and responds with a lower resonance frequency. We show that this soft mode can be…
Introducing a Kerr medium in a cavity coupled to a harmonically moving mirror, we reproduce known and solvable interactions such as two-coupled harmonic oscillators and ion-laser like interactions for specific conditions. This is achieved by a unitary transformation allowing us to tune off the Kerr medium in order to simplify the Hamiltonian.
Few-photon optomechanical effects are not only important physical evidences for understanding the radiation-pressure interaction between photons and mechanical oscillation, but also have wide potential applications in modern quantum technology. Here we study the few-photon optomechanical effects including photon blockade and generation of the Schrödinger cat states under the assistance of a cross-Kerr interaction, which is an inherent interaction accompanied the optomechanical coupling in a generalized optomechanical system. By exactly diagonalizing the generalized optomechanical Hamiltonian a…
Ultracold bosonic atoms in optical lattices self-organize into a variety of structural and quantum phases when placed into a single-mode cavity and pumped by a laser. Cavity optomechanical effects induce an atom density modulation at the cavity-mode wave length that competes with the optical lattice arrangement. Simultaneously short-range interactions via particle hopping promote superfluid order, such that a variety of structural and quantum coherent phases can occur. We analyze the emerging phase diagram in two dimensions by means of an extended Bose-Hubbard model using a local mean field ap…
Low dissipation, tunable coupling to other quantum systems, and unique features of phonons in the aspects of propagation, detection and others suggest the applications of quantized mechanical resonators in phonon-based quantum information processing (QIP) in a way different from their photonic counterpart. In this paper, we propose the first protocol of entanglement concentration for nonlocal phonons from quantized mechanical vibration. We combine the optomechanical cross-Kerr interaction with the Mach-Zehnder interferometer and, by means of twice optomechanical interactions and the photon ana…
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 …
Nonreciprocal devices are indispensable for building quantum networks and ubiquitous in modern communication technology. Here, we use optomechanical interaction and linearly-coupled interaction to realize optical nonreciprocal transmission in a double-cavity optomechanical system. The scheme relies on the interference between the two interactions. We derive the essential conditions to realize perfect optical nonreciprocity in the system, and analyse the properties of optical nonreciprocal transmission and the output fields from mechanical mode. These results can be used to control optical tran…
We study an optomechanical system consisting of an optical cavity and movable mirror coupled through dispersive linear optomechanical coupling (LOC) and quadratic optomechanical coupling(QOC). We work in the resolved side band limit with a high quality factor mechanical oscillator in a strong coupling regime. We show that the presence of QOC in the conventional optomechanical system (with LOC alone) modifies the mechanical oscillator's frequency and reduces the back-action effects on mechanical oscillator. As a result of this the fluctuations in mechanical oscillator can be suppressed below st…
The realization of multimode optomechanical interactions in the single-photon strong-coupling regime is a desired task in cavity optomechanics, but it remains a challenge in realistic physical systems. In this work, we propose a reliable scheme to simulate a three-mode optomechanical system working in the single-photon strong-coupling regime based on the Fredkin-type interaction. This is achieved by utilizing two strong drivings to the two exchangly-coupled modes in the Fredkin-type coupling involving one optical mode and two mechanical-like modes. As an application of this enhanced three-mode…
We show that single-mode nonclassicality of the output of an optomechanical cavity and the noncausal linear optical response of this cavity emerge at the same critical cavity-mechanical coupling. In other words, single-mode nonclassicality emerges when the barrier (in electromagnetism) avoiding faster-than-light communication is lifted off. The nature of the emergence of noncausal behavior does not depend on the length (boundary conditions) and the type of the cavity. Origin of the noncausal behavior is the temporal/frequency relations between the incident and reflected waves at the outer surf…
We realise a feedback-controlled optical Fabry-Perot cavity in which the transmitted cavity output is used to modulate the input amplitude fluctuations. The resulting phase-dependent fluctuations of the in-loop optical field, which may be either sub-shot- or super-shot-noise, can be engineered to favorably affect the optomechanical interaction with a nanomechanical membrane placed within the cavity. Here we show that in the super-shot-noise regime ("anti-squashed light") the in-loop field has a strongly reduced effective cavity linewidth, corresponding to an increased optomechanical cooperativ…
We investigate the resonant enhancement of nonlinear interactions in a three-mode cavity optomechanical system with two mechanical oscillators. By using the Keldysh Green's function technique we find that nonlinear effects on the cavity density of states can be greatly enhanced by the resonant scattering of two phononic polaritons, due to their small effective dissipation. In the large detuning limit and taking into account an upper bound on the achievable dressed coupling, the optimal point for probing the nonlinear effect is obtained, showing that such three-mode system can exhibit prominent…
We use single photon detectors to probe the motional state of a superfluid $^4$He resonator of mass $\sim1$ ng. The arrival times of Stokes and anti-Stokes photons (scattered by the resonator's acoustic mode) are used to measure the resonator's phonon coherences up to the fourth order. By post-selecting on photon detection events, we also measure coherences in the resonator when $\leq3$ phonons have been added or subtracted. These measurements are found to be consistent with predictions that assume the acoustic mode to be in thermal equilibrium with a bath through a Markovian coupling.
We study the spectrum of single-photon emission and scattering in a mixed optomechanical model which consists of both linear and quadratic optomechanical interactions. The spectra are calculated based on the exact long-time solutions of the single-photon emission and scattering processes in this system. We find that there exist some phonon sideband peaks in the spectra and there are some sub peaks around the phonon sideband peaks under proper parameter conditions. The correspondence between the spectral features and the optomechanical interactions is confirmed, and the optomechanical coupling …
Optomechanical systems provide a means for studying and controlling quantum effects in the motion of macroscopic objects. To date, quantum optomechanical effects have been studied in objects made from solids and gases. Here we describe measurements of quantum behavior in the vibrations of a liquid body. Specifically, we monitor the fluctuations of an individual acoustic standing wave in superfluid liquid helium, and find that it displays the characteristic signatures of zero-point motion and measurement back-action. This opens the possibility of exploiting the properties of liquids in general …
We explore the electromagnetic field coupled to a mechanical resonator via quadratic optomechanical interaction in the reversed dissipation regime where the mechanical damping rate is much larger than the cavity field dissipation rate. It is shown that in this regime, the cavity field effectively acquires an additional reservoir which is conditioned by the temperature of the mechanical bath as well as the mechanical damping rate. We analytically find the steady-state mean photon number and the critical temperature of the mechanical oscillator to cool or heat the coupled electromagnetic field. …
We propose using optomechanical interaction to narrow the bandwidth of filter cavities for achieving frequency-dependent squeezing in advanced gravitational-wave detectors, inspired by the idea of optomechanically induced transparency. This not only allows us to achieve narrow bandwidth, comparable to the detection band of few hundred Hz, with tabletop optical cavities, but also to tune the bandwidth over a wide range, which is ideal for optimizing sensitivity for different gravitational-wave sources. The experimental challenge for its implementation is the stringent requirement on low thermal…
We theoretically investigate the emission spectrum of an optomechanical Tavis-Cummings model: two dipole-dipole interacting atoms coupled to an optomechanical cavity (OMC). In particular, we study the influence of dipole-dipole interaction (DDI) on the single-photon spectrum emitted by this hybrid system in the presence of a strong atom-cavity as well as strong optomechanical interaction (hereinafter called the strong-strong coupling). We also show that our analysis is amenable to inclusion of mechanical losses (under the weak mechanical damping limit) and single-photon loss through spontaneou…
A nonlocal circulator protocol is proposed in hybrid optomechanical system. By analogy with quantum communication, using the input-output relationship, we establish the quantum channel between two optical modes with long-range. The three body nonlocal interaction between the cavity and the two oscillators is obtained by eliminating the optomechanical cavity mode and verifying the Bell-CHSH inequality of continuous variables. By introducing the phase accumulation between cyclic interactions, the unidirectional transmission of quantum state between optical mode and two mechanical modes are achie…
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…
Phonon nonlinearities play an important role in hybrid quantum networks and on-chip quantum devices. We investigate the phonon statistics of a mechanical oscillator in hybrid systems composed of an atom and one or two standard optomechanical cavities. An efficiently enhanced atom-phonon interaction can be derived via a tripartite atom-photon-phonon interaction, where the atom-photon coupling depends on the mechanical displacement without practically changing a cavity frequency. This novel mechanism of optomechanical interactions, as predicted recently by Cotrufo et al. [Phys. Rev. Lett. 118, 1…
The search for new control methods over light-matter interactions is one of the engines that advances fundamental physics and applied science alike. A specific class of light-matter interaction interfaces are setups coupling photons of distinct frequencies via matter. Such devices, nontrivial in design, could be endowed with multifunctional tasking. Here we envisage for the first time an optomechanical system that bridges optical and robust, high-frequency x-ray photons, which are otherwise notoriously difficult to control. The x-ray-optical system comprises of an optomechanical cavity and a m…
We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and he…
A scheme of single-photon multi-port router is put forward by coupling two optomechanical cavities with waveguides. It is shown that the coupled two optomechanical cavities can exhibit photon blockade effect, which is generated from interference of three mode interaction. A single-photon travel along the system is calculated. The results show that the single photon can be controlled in the multi-port system because of the radiation pressure, which should be useful for constructing quantum network.
The generation of entangled states that display negative values of the Wigner function in the quantum phase space is a challenging task, particularly elusive for massive, and possibly macroscopic, systems such as mechanical resonators. In this work, we propose two schemes based on reservoir engineering for generating Wigner-negative entangled states unconditionally. We consider two non-interacting mechanical resonators that are radiation-pressure coupled to either one or two common cavity fields; the optomechanical coupling with the field(s) features both a linear and quadratic part in the mec…
With a perturbative treatment based on the Keldysh Green's function technique, we study the resonant enhancement of nonlinear interaction effects in a four-mode optomechanical ring. In such a system, we identify five distinct types of resonant scattering between unperturbed polariton modes, induced by the nonlinear optomechanical interaction. By computing the cavity density of states and optomechanical induced transparency signal, we find that the largest nonlinear effects are induced by a decay process involving the two phonon-like polaritons. In contrast to the conventional two-mode optomech…
Squeezing of quantum fluctuation plays an important role in fundamental quantum physics and has marked influence on ultrasensitive detection. We propose a scheme to generate and enhance the squeezing of mechanical mode by exposing the optomechanical system to a non-Markovian environment. It is shown that the effective parametric resonance term of mechanical mode can be induced due to the interaction with cavity and non-Markovian reservoir, thus resulting in quadrature squeezing of the mechanical resonator. And jointing the two kinds of interactions can enhance the squeezing effect. Comparing w…
Optomechanical systems are rapidly becoming one of the most promising platforms for observing quantum behaviour, especially at the macroscopic level. Moreover, thanks to their state-of-the-art methods of fabrication, they may now enter regimes of non-linear interactions between their constituent mechanical and optical degrees of freedom. In this work, we show how this novel opportunity may serve to construct a new generation of optomechanical sensors. We consider the canonical optomechanical setup with the detection scheme being based on time-resolved counting of photons leaking from the cavit…
We investigate the spectrum of energy and eigenstates of a hybrid cavity optomechanical system, where a cavity field mode interacts with a mechanical mode of a vibrating end mirror via radiation pressure and with a two level atom via electric dipole interaction. In the spirit of approximations developed for the quantum Rabi model beyond rotating-wave approximation (RWA), we implement the so-called generalized RWA (GRWA) to diagonalize the tripartite Hamiltonian for arbitrary large couplings. Notably, the GRWA approach still allows to rewrite the hybrid Hamiltonian in a bipartite form, like a R…
In this work we study an optomechanical system in which there is a purely quadratic optomechanical coupling between the optical and mechanical modes. The optical mode is pumped by three coherent fields and the mechanical mode is parametrically driven. We show that if the frequencies and amplitudes of both optical and mechanical drivings are properly chosen, the optomechanical interaction gives rise to an effective interaction, which, in the presence of optical damping and in the absence of mechanical damping, has the squeezed vacuum state and the squeezed one phonon state as dark states of the…
Probing gravitational interaction between milligram optomechanical oscillators operating in the quantum regime
Istituto Nazionale di Fisica Nucleare, TIFPA（意大利国家核物理研究所，TIFPA）；Institute of Materials for Electronics and Magnetism, Nanoscience-Trento-FBK Division（电子与磁性材料研究所，纳米科学-特伦托FBK分部）；Physics Division, School of Science and Technology, Università di Camerino（卡梅里诺大学理学院物理系）；INFN, Sezione di Perugia（意大利国家核物理研究所，佩鲁加分部）；LENS（激光工程与应用科学欧洲研究中心）；Dipartimento di Fisica e Astronomia, Università di Firenze（佛罗伦萨大学物理与天文学系）；INFN, Sezione di Firenze（意大利国家核物理研究所，佛罗伦萨分部）；CNR-INO（意大利国家研究委员会-光学研究所）
In general, ground state cooling using optomechanical interaction is realized in the regime where optical dissipation is higher than mechanical dissipation. Here, we demonstrate that optomechanical ground state cooling in a continuous optomechanical system is possible by using backward Brillouin scattering while mechanical dissipation exceeds optical dissipation which is the common case in optical waveguides. The cooling is achieved in an anti-Stokes backward Brillouin process by modulating the intensity of the optomechanical coupling via a pulsed pump to suppress heating processes in the stro…
We examine the entanglement properties of a system that represents two driven microwave cavities each optomechanically coupled to two separate driven optical cavities which are connected by a single-mode optical fiber. The results suggest that it may be possible to achieve near-maximal entanglement of the microwave cavities, thus allowing a teleportation scheme to enable interactions for hybrid quantum computing of superconducting qubits with optical interconnects.
Quantum phase synchronisation enhanced via Coulomb interaction in an optomechanical system
University of Yaounde I（雅温得第一大学）；University of Ngaoundere（恩冈德雷大学）；Nantong University（南通大学）；Government College University（政府学院大学）；IIT Kharagpur（印度理工学院卡拉格普尔分校）；University of Bisha（比沙大学）；Akal University（阿卡尔大学）
We study tunable optomechanically induced transparency by controlling the dark-mode effect induced by two mechanical modes coupled to a common cavity field. This is realized by introducing a phase-dependent phonon-exchange interaction, which is used to form a loop-coupled configuration. Combining this phase-dependent coupling with the optomechanical interactions, the dark-mode effect can be controlled by the quantum interference effect. In particular, the dark-mode effect in this two-mechanical-mode optomechanical system can lead to a double-amplified optomechanically induced transparency (OMI…
In this paper we consider the quantum repeater protocol for distributing the entanglement to two distant three-level atoms. In this protocol, we insert six atoms between two target atoms such that the eight considered atoms are labeled by 1; 2;... 8, while only each two adjacent atoms (i; i + 1) with i = 1; 3; 5; 7 are entangled. Initially, the separable atomic pair states (1,4) and (5,8) become entangled by performing interaction between atoms (2,3) and (6,7) in two optomechanical cavities, respectively. Then, via performing appropriate interaction between atoms (4,5) in an optical cavity qua…
We demonstrate optomechanical interference in a multimode system, in which an optical mode couples to two mechanical modes. A phase-dependent excitation-coupling approach is developed, which enables the observation of constructive and destructive optomechanical interferences. The destructive interference prevents the coupling of the mechanical system to the optical mode, suppressing optically-induced mechanical damping. These studies establish optomechanical interference as an essential tool for controlling the interactions between light and mechanical oscillators.
We propose using the optomechanical interaction to create artificial magnetic fields for photons on a lattice. The ingredients required are an optomechanical crystal, i.e. a piece of dielectric with the right pattern of holes, and two laser beams with the right pattern of phases. One of the two proposed schemes is based on optomechanical modulation of the links between optical modes, while the other is an lattice extension of optomechanical wavelength-conversion setups. We illustrate the resulting optical spectrum, photon transport in the presence of an artificial Lorentz force, edge states, a…
We propose a scheme to prepare a macroscopic mechanical oscillator in a catlike state, close to a coherent state superposition. The mechanical oscillator, coupled by radiation-pressure interaction to a field in an optical cavity, is first prepared close to a squeezed vacuum state using a reservoir engineering technique. The system is then probed using a short optical pulse tuned to the lower motional sideband of the cavity resonance, realizing a photon-phonon swap interaction. A photon number measurement of the photons emerging from the cavity then conditions a phonon-subtracted catlike state …
We theoretically investigate the dispersive interaction of a Bose-Einstein condensate (BEC) trapped inside an optomechanical cavity with a moving end mirror in the presence of the laser phase noise (LPN) as well as the atomic collisions. We assume that the effective frequency of the optical mode is much greater than those of the mechanical and the Bogoliubov modes of the movable mirror and the BEC . In the adiabatic approximation where the damping rate of the cavity is faster than those of the other modes, the system behaves as an effective two-mode model in which the atomic and mechanical mod…
