Ultra-precision quantum sensing and measurement based on nonlinear hybrid optomechanical systems containing ultracold atoms or atomic Bose-Einstein condensate
Ali Motazedifard, A. Dalafi, M. H. Naderi
备注：
Accepted at AVS Quantum Science in AIP publishing for a review collection Book on Quantum Sensing and Metrology. It was an invited article from AVS AIP publishing. Also, It has been chosen as "Editor's Pick"; 32 pages; 12 figures
In this review, we study how a hybrid optomechanical system (OMS), in which a quantum micro- or nano-mechanical oscillator (MO) is coupled to the electromagnetic (EM) radiation pressure, consisting of an ensemble of ultracold atoms or an atomic Bose-Einstein condensate (BEC), can be used as an ultra precision quantum sensor for measuring very weak signals. As is well-known in any precise quantum measurement the competition between the shot noise (SN) and the backaction noise of measurement executes a limitation on the measurement precision which is the so-called standard quantum limit (SQL). In the case where the intensity of the signal is even lower than the SQL, one needs to perform an ultra precision quantum sensing to beat the SQL. For this purpose, we review three important methods for surpassing the SQL in a hybrid OMS: (i) the backaction evading measurement of a quantum nondemolition (QND) variable of the system, (ii) the coherent quantum backaction noise cancellation (CQNC), and (iii) the so-called parametric sensing, the simultaneous signal amplification and added noise suppression below the SQL. Furthermore, we have shown in this article for the first time how the classical fluctuation of the driving laser phase, the so-called laser phase noise (LPN), affects the power spectrum of the output optical field in a standard OMS and induces an additional impression noise which makes the total system noise increase above the SQL. Also, for the first time in this review it has been shown that in the standard OMSs, it is impossible to amplify signal while suppressing the noise below the SQL simultaneously.
In this paper we describe a scheme for state transfer between a trapped atomic Bose condensate and an optomechanical end-mirror mediated by a cavity field. Coupling between the mirror and the cold gas arises from the fact that the cavity field can produce density oscillations in the gas which in turn acts as an internal Bragg mirror for the field. After adiabatic elimination of the cavity field we find that the hybrid system of the gas and mirror is described by a beam splitter Hamiltonian that allows for state transfer, but only if the quantum nature of the cavity field is retained.
We have realized a hybrid optomechanical system by coupling ultracold atoms to a micromechanical membrane. The atoms are trapped in an optical lattice, which is formed by retro-reflection of a laser beam from the membrane surface. In this setup, the lattice laser light mediates an optomechanical coupling between membrane vibrations and atomic center-of-mass motion. We observe both the effect of the membrane vibrations onto the atoms as well as the backaction of the atomic motion onto the membrane. By coupling the membrane to laser-cooled atoms, we engineer the dissipation rate of the membrane.…
We investigate theoretically a hybrid system consisting of a Bose-Einstein condensate (BEC) trapped inside a laser driven membrane-in-the-middle optomechanical cavity assisted with squeezed vacuum injection whose moving membrane interacts both linearly and quadratically with the radiation pressure of the cavity. It is shown that such a hybrid system is very suitable for generating strong quadrature squeezing in the mechanical mode of the membrane and the Bogoliubov mode of the BEC in the unresolved sideband regime. More interestingly, by choosing a suitable sign for the quadratic optomechanica…
We analyze a detailed model of a Bose-Einstein condensate trapped in a ring optical resonator and contrast its classical and quantum properties to those of a Fabry-P{é}rot geometry. The inclusion of two counter-propagating light fields and three matter field modes leads to important differences between the two situations. Specifically, we identify an experimentally realizable region where the system's behavior differs strongly from that of a BEC in a Fabry-Pérot cavity, and also where quantum corrections become significant. The classical dynamics are rich, and near bifurcation points in the me…
We study theoretically a driven hybrid optomechanical system with a membrane-in-the-middle configuration containing two identical elongated cigar-shaped Bose-Einstein condensates (BECs) in each side of the membrane. In the weakly interacting regime, the BECs can be considered as single-mode oscillators in the Bogoliubov approximation which are coupled to the optical field through the radiation pressure interaction so that they behave as two quasi-membranes. We show that the degree of squeezing of each BEC and its entanglement with the moving membrane can be controlled by the \textit{s}-wave sc…
We investigate a hybrid quantum system consisting of a cavity optomechanical device optically coupled to an ultracold quantum gas. We show that the dispersive properties of the ultracold gas can be used to dramatically modify the optomechanical response of the mechanical resonator. We examine hybrid schemes wherein the mechanical resonator is coupled either to the motional or the spin degrees of freedom of the ultracold gas. In either case, we find an enhancement of more than two orders of magnitude in optomechanical cooling due to this hybrid interaction. Significantly, based on demonstrated …
In this paper, we study theoretically the optomechanical interaction of an almost pure condensate of photons with an oscillating mechanical membrane in a micro-cavity. We show that in the Bogoliubov approximation, due to the large number of photons in the condensate phase, there is a linear strong effective coupling between the Bogoliubov mode of the photonic Bose-Einstein condensate (BEC) and the mechanical motion of the membrane which depends on the nonlinear photon-photon scattering potential. This coupling leads to the cooling of the mechanical motion, the normal mode splitting (NMS), the …
Schrödinger cat states, consisting of superpositions of macroscopically distinct states, provide key resources for a large number of emerging quantum technologies in quantum information processing. Here we propose how to generate and manipulate mechanical and optical Schrödinger cat states with distinguishable superposition components by exploiting the unique properties of cavity optomechanical systems based on Bose-Einstein condensate. Specifically, we show that in comparison with its solid-state counterparts, almost a $3$ order of magnitude enhancement in the size of the mechanical Schröding…
Preparing and manipulating quantum states of mechanical resonators is a highly interdisciplinary undertaking that now receives enormous interest for its far-reaching potential in fundamental and applied science. Up to now, only nanoscale mechanical devices achieved operation close to the quantum regime. We report a new micro-optomechanical resonator that is laser cooled to a level of 30 thermal quanta. This is equivalent to the best nanomechanical devices, however, with a mass more than four orders of magnitude larger (43 ng versus 1 pg) and at more than two orders of magnitude higher environm…
Various lower- and higher-order nonclassical properties have been studied for two physical systems- (i) an optomechanical system composed of a Fabry-Perot cavity with one nonlinearly oscillating mirror and (ii) an optomechanical-like system formed using a Bose-Einstein condensate (BEC) trapped inside an optical cavity. The investigation is performed using a perturbation method that leads to closed form analytic expressions for the time evolution of the relevant bosonic operators. In the first system, it is observed that the radiation pressure coupling leads to the emergence of lower- and highe…
We analyze an atomic Bose-Einstein condensate trapped in a high-Q optical cavity driven by a feeble optical field, a situation formally analogous to the central paradigm of cavity optomechanics [Brennecke et al., Science, 322, 235 (2008)]. We account for two-body interactions via a two-fluid model that retains the intuitive appeal of the optomechanical two-mode description. The Bogoliubov excitation spectrum of this system comprises a gapped upper branch and a lower branch that can include an unstable excitation mode.
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…
We consider an optomechanical cavity with a movable end-mirror as a quantum mechanical oscillator (MO) containing an interacting cigar-shaped Bose-Eisenstein condensate (BEC). It is assumed that both the MO and the BEC interact with the radiation pressure of the cavity field in the red-detuned and weak coupling regimes while the two-body atomic collisions frequency of the BEC and the mechanical spring coefficient of the MO are coherently modulated. By analyzing the scattering matrix we find that a frequency-dependent squeezing is induced to the three subsystems only due to the coherent modulat…
In many experiments isolated atoms and ions have been inserted into high-finesse optical resonators for the study of fundamental quantum optics and quantum information. Here, we introduce another application of such a system, as the realization of cavity optomechanics where the collective motion of an atomic ensemble serves the role of a moveable optical element in an optical resonator. Compared with other optomechanical systems, such as those incorporating nanofabricated cantilevers or the large cavity mirrors of gravitational observatories, our cold-atom realization offers direct access to t…
We present a detailed study to analyse the Dicke quantum phase transition within the thermodynamic limit for an optomechanically driven Bose-Einstein condensates in a cavity. The photodetection-based quantum optical measurements have been performed to study the dynamics and excitations of this optomechanical Dicke system. For this, we discuss the eigenvalue analysis, fluorescence spectrum and the homodyne spectrum of the system. It has been shown that the normal phase is negligibly affected by the mechanical mode of the mirror while it has a significant effect in the superradiant phase. We hav…
We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose-Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions. The cavity frequency is harmonically modulated in time for both the cases. The main quantity of interest is the number of intracavity scattered photons. The system has been investigated under the weak and strong modulation. It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion. Also, initially, th…
We investigate the dynamical phase transition of two-component Bose-Einstein condensate with nonlinear tunneling, which is trapped inside a double-well and dispersively coupled to a single mode of a high-finesse optical cavity with one moving end mirror driven by a single mode standing field. The nonlinear tunneling interaction leads to an increase of stability points and riches the phase diagram of the system. It is shown that the appearance of the moving end mirror speeds up the tunneling of Bose-Einstein condensates, which makes population difference between two wells and regulates the numb…
We propose to thermalize a low-dimensional photon gas and obtain photon Bose-Einstein condensation by optomechanical interactions in a microscopic optical cavity, with a single longitudinal mode and many transverse modes. The geometry of the short cavity is such that it provides a low-frequency cutoff at a photon energy far above the thermal energy, so that thermal emission of photons is suppressed and the photon number is conserved. While previous experiments on photon Bose-Einstein condensation have used dye molecules for photon gas thermalization, we here investigate thermalization owing to…
We consider a cavity optomechanical system consisting of a Bose-Einstein condensate (BEC) interacting with two counterpropagating traveling-wave modes in an optical ring cavity. In contrast to the more familiar case where the condensate is driven by the standing-wave field of a high-$Q$ Fabry-P{é}rot cavity we find that both symmetric and antisymmetric collective density side modes of the BEC are mechanically excited by the light field. In the semiclassical, mean-field limit where the light field and the zero-momentum mode of the condensate are treated classically the system is found to exhibi…
We propose that the dispersion management of coherent atomic matter waves can be exploited to overcome quantum back-action in condensate-based optomechanical sensors. The effective mass of an atomic Bose-Einstein condensate modulated by an optical lattice can become negative, resulting in a negative-frequency optomechanical oscillator, a negative environment temperature, and optomechanical properties opposite to those of a positive-mass system. This enables a quantum-mechanics-free subsystem insulated from quantum back-action.
We present the rigorous microscopic quantum theory of the interaction of ultracold Bose and Fermi gases with the electromagnetic field of vacuum and laser photons. The main attention has been paid to the consistent consideration of dynamical dipole-dipole interactions. The theory developed is shown to be consistent with the general principles of the canonical quantization of electromagnetic field in a medium. Starting from the first principles of QED we have derived the general system of Maxwell-Bloch equations for atomic creation and annihilation operators and the propagation equation for the…
The optical bistability (OB) in a two-mode optomechanical system with a Bose-Einstein condensate (BEC) is studied. By investigating the behavior of steady state solutions, we show that how OB develops in the system for a certain range of cavity-pump detunings and pump amplitudes. We then investigate the effects of the decay rate of the cavity photons and coupling strength between the cavity and the BEC as well as the pump-atom detuning on the optical behaviour of the system. We find that one can control the OB threshold and width of the bistability curve via adjusting properly the decay rate, …
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We investigate a system consisting of a two-component Bose-Einstein condensate interacting dispersively with a Fabry-Perot optical cavity where the two components of the condensate are resonantly coupled to each other by another classical field. The key feature of this system is that the atomic motional degrees of freedom and the internal pseudo-spin degrees of freedom are coupled to the cavity field simultaneously, hence an effective spin-orbital coupling within the condensate is induced by the cavity. The interplay among the atomic center- of-mass motion, the atomic collective spin and the c…
We analyze the optomechanics-like properties of a Bose-Einstein condensate (BEC) trapped inside an optical resonator and driven by both a classical and a quantized light field. We find that this system exhibits a nature of role reversal between the matter-wave field and the quantized light field. As a result, the matter wave field now plays the role of the quantized light field, and the quantized light field behaves like a movable mirror, in contrast to the familiar situation in BEC-based cavity optomechanics [Brennecke et al., Science 322, 235 (2008); Murch et al., Nat. Phys. 4, 561 (2008)]. …
We consider a hybrid atom-optomechanical system consisting of a mechanical membrane inside an optical cavity and an atomic Bose-Einstein condensate outside the cavity. The condensate is confined in an optical lattice potential formed by a traveling laser beam reflected off one cavity mirror. We derive the cavity-mediated effective atom-atom interaction potential, and find that it is non-uniform, site-dependent, and does not decay as the interatomic distance increases. We show that the presence of this effective interaction breaks the Z$_2$ symmetry of the system and gives rise to new quantum p…
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We investigate theoretically the effect of optical feedback from a cavity containing an ultracold two level atomic ensemble, on the bistable behavior shown by mean intracavity optical field and the ground state cooling effect of the mechanical oscillator in an optomechanical cavity resonator. The optical bistability can be controlled by tuning the frequency and power of the single driving laser as well as by varying the atom-cavity coupling strength in the atomic cavity. Study of the cooling of the mechanical oscillator, in both good and bad cavity limits, reveals that the hybrid system is mor…
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We investigate theoretically the effect of optical feedback from a cavity containing an ultracold two level atomic ensemble, on the bistable behavior shown by mean intracavity optical field in an optomechanical cavity resonator. It turns out that the optical bistability can be controlled by tuning the frequency and power of the driving laser and is largely affected by the presence of the atomic ensemble in the feedback cavity. In essence, our work emphasizes the possibility of realization of a controllable optical switch depending on the hybrid interaction, commanding lower threshold power tha…
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We demonstrate the control of entanglement in a hybrid optomechanical system comprising an optical cavity with a mechanical end-mirror and an intracavity Bose-Einstein condensate (BEC). Pulsed laser light (tuned within realistic experimental conditions) is shown to induce an almost sixfold increase of the atom-mirror entanglement and to be responsible for interesting dynamics between such mesoscopic systems. In order to assess the advantages offered by the proposed control technique, we compare the time-dependent dynamics of the system under constant pumping with the evolution due to the modul…
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