We explore the relative robustness of squeezing and entanglement (which are quantum resources interconvertible via passive optics) for two-mode Gaussian states under different dissipative environments. When the individual modes interact with identical local baths, entanglement and squeezing decay at the same rate. However, when only one of the modes interacts with a local bath, the comparative robustness of entanglement and squeezing depends on the initial squeezing of the state. Similarly, when the system interacts with a global bath, the robustness of entanglement and squeezing depends on the initial squeezing. Thus depending on the nature of dissipative environments and the initial squeezing of the state, one can select the more robust form of resource out of squeezing and entanglement to store quantumness. This can be used to effectively enhance the performance of various quantum information processing protocols based on continuous variable Gaussian states.
We investigate the steady-state photon-number squeezing and quantum entanglement in a network of nondegenerate optical parametric oscillators (NOPOs). We treat each NOPO with Shen's Raman laser model, whose lasing mode provides a photon-number-squeezed state. Two dissipatively coupled NOPOs satisfy Hillery-Zubairy's $HZ1$ entanglement criterion if they are pumped far above the threshold and the dissipative coupling is sufficiently larger than the NOPO cavity loss.
Based on the time-convolutionless master-equation approach, we investigate squeezing of light field in a dissipative Jaynes-Cummings model. The results show that squeezing light can be generated when the atom transits to a ground state from an excited state, and then a collapse-revival phenomenon will occur in the squeezing of light field due to atom-cavity coupling. Enhancing the atom-cavity coupling can increase the frequency of the collapse-revival of squeezing. The stronger the non-Markovian effect is, the more obvious the collapse-revival phenomenon is. The oscillatory frequency of the sq…
Quantum squeezing of mechanical resonator is important for studying the macroscopic quantum effects and the precision metrology of weak forces. Here we give a theoretical study of a hybrid atom-optomechanical system in which the steady-state squeezing of the mechanical resonator can be generated via the mechanical nonlinearity and cavity cooling process. The validity of the scheme is assessed by simulating the steady-state variance of the mechanical displacement quadrature numerically. The scheme is robust against dissipation of the optical cavity, and the steady-state squeezing can be effecti…
We investigate spin squeezing for a Lipkin-Meshkov-Glick (LMG) model coupled to a general non-Markovian environment in a finite temperature regime. Using the non-Markovian quantum state diffusion and master equation approach, we numerically study non-Markovian spin squeezing generation in LMG model. Our results show that the total spin number N, energy kBT, and certain coefficients in a LMG model can play a crucial role in generating spin squeezing. In particular, it shows that the maximum spin squeezing can be significantly enhanced when the participating environment has a relatively long mem…
We investigate the squeezed regions in the phase plane for non-dissipative dynamical systems controlled by SU(1,1) Lie algebra. We analyze such study for the two SU(1,1) generalized coherent states, namely, the Perelomov coherent state (PCS) and the Barut-Girardello Coherent state (BGCS).
We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i) taking into account explicitly, through a collective variable description, the drift of the dissipative structure caused by the quantum noise, and (ii) expanding the remaining -internal- fluctuations in the biorthonormal basis associated to the linear operator governing the evolution of fluctuations in the linearized Langevin equations. We obtain general expres…
Spin squeezing of collective atomic spins can be achieved conditionally via probing with light and subsequent homodyne detection, as is done in a Quantum Nondemolition measurement. Recently it has been shown that squeezing can also be created unconditionally by a properly designed dissipative dynamics. We compare the two approaches in a Gaussian description, and optimize over all Gaussian light-matter interactions. We find that in the optimal unconditional scheme based on dissipation the level of squeezing scales as $d^{-1/2}$. In contrast, the optimal conditional scheme based on measurement o…
Squeezed states of spin systems are an important entangled resource for quantum technologies, particularly quantum metrology and sensing. Here we consider the generation of spin squeezed states by interacting the spins with a dissipative ancillary system. We show that spin squeezing can be generated in this model by two different mechanisms: one-axis twisting and driven collective relaxation. We can interpolate between the two mechanisms by simply adjusting the detuning between the dissipative ancillary system and the spin system. Interestingly, we find that for both mechanisms, ancillary syst…
We investigate a hybrid system consisting of an atomic ensemble trapped inside a dissipative optomechanical cavity assisted with the perturbative oscillator-qubit coupling. It is shown that such a hybrid system is very suitable for generating stationary squeezing of the mirror motion in the long-time limit under the unresolved sideband regime. Based on the approaches of master equation and covariance matrix, we discuss the respective squeezing effects in detail and find that in both approaches, simplifying the system dynamics with adiabatic elimination of the highly dissipative cavity mode is …
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 s…
We systematically study the influence of amplitude modulation on the steady-state bosonic squeezing and entanglement in a dissipative three-mode optomechanical system, where a vibrational mode of the membrane is coupled to the left and right cavity modes via the radiation pressure. Numerical simulation results show that the steady-state bosonic squeezing and entanglement can be significantly enhanced by periodically modulated external laser driving either or both ends of the cavity. Remarkably, the fact that as long as one periodically modulated external laser driving either end of the cavitie…
While a propagating state of light can be generated with arbitrary squeezing by pumping a parametric resonator, the intra-resonator state is limited to 3 dB of squeezing. Here, we implement a reservoir engineering method to surpass this limit using superconducting circuits. Two-tone pumping of a three-wave-mixing element implements an effective coupling to a squeezed bath which stabilizes a squeezed state inside the resonator. Using an ancillary superconducting qubit as a probe allows us to perform a direct Wigner tomography of the intra-resonator state. The raw measurement provides a lower bo…
We investigate the squeezing for a movable mirror in the dissipative optomechanics in which the oscillating mirror modulates both the resonance frequency and the linewidth of the cavity mode. Via feeding a much weaker broadband squeezed vacuum light accompanying the coherent driving laser field into the cavity, the master equation for the cavity-mirror system is derived by following the general reservoir theory based on the density operator in which the reservoir variables are adiabatically eliminated by using the reduced density operator for the system in the interaction picture. When the mir…
The recent demonstration of cooling of a macroscopic silicon nitride membrane based on dissipative coupling makes dissipatively coupled optomechanical systems as promising candidates for squeezing. We theoretically show that such a system in a cavity on resonance can yield good squeezing which is comparable to that produced by dispersive coupling. We also report the squeezing resulting from the combined effects of dispersive and dissipative couplings and thus the device can be operated in one regime or the other. We derive the maximal frequency and quadrature angles to observe squeezing for gi…
We show that any optical dissipative structure supported by degenerate optical parametric oscillators contains a special transverse mode that is free from quantum fluctuations when measured in a balanced homodyne detection experiment. The phenomenon is not critical as it is independent of the system parameters and, in particular, of the existence of bifurcations. This result is a consequence of the spatial symmetry breaking introduced by the dissipative structure. Effects that could degrade the squeezing level are considered.
We discuss a simple yet surprisingly effective mechanism which allows the generation of squeezed output light from an optomechanical cavity. In contrast to the well known mechanism of "ponderomotive squeezing", our scheme generates squeezed output light by explicitly using the dissipative nature of the mechanical resonator. We show that our scheme has many advantages over ponderomotive squeezing; in particular, it is far more effective in the good cavity limit commonly used in experiments. Furthermore, the squeezing generated in our approach can be directly used to enhance the intrinsic measur…
We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fibre, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibres. The research represents a significant experimental test of first-principles time-domain quantum dy…
We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the signal-to-noise ratio to quantify the sensitivity of linear spectral measurements. Then, we consider stationary force sensing and study the necessary conditions to minimise the added force noise. We find that imprecision noise and back-action noise can be arbitrarily suppressed by manipulating the amplitudes of the input coherent fields, however, the force noise p…
We study the transverse-field Ising model with infinite-range coupling and spontaneous emission on every site. We find that there is spin squeezing in steady state due to the presence of the transverse field. This means that there is still entanglement, despite the decoherence from spontaneous emission. We analytically calculate fluctuations beyond mean-field theory using a phase-space approach, which involves converting the master equation into a Fokker-Planck equation for the Wigner function. Our calculations are relevant to current experiments with trapped ions.
This dissertation studies spin squeezing, entanglement and decoherence in large ensembles of cold, trapped alkali atoms with hyperfine spin f interacting with optical fields. Restricting the state of each atom to a qutrit embedded in the 2f+1 dimensional hyperfine spin enables us to efficiently model the coherent and dissipative dynamics of the ensemble. This formalism also allows us to explore the effects of local control on the internal hyperfine spins of the atoms. State preparation using such control increases the entangling power of the atom-light interface for f>1/2. Subsequent control o…
We study the XY model with infinite-range interactions (Lipkin-Meshkov-Glick model) in the presence of dissipation from spontaneous decay. We show that independent and collective decay lead to qualitatively different phase transitions of the steady state, even though the phase boundary is the same. Independent decay leads to a second-order phase transition to a ferromagnet, while collective decay leads to a first-order transition to a time-dependent oscillatory phase. Then we show that the addition of a drive leads to infinite spin squeezing for collective decay in the thermodynamic limit. Our…
Single-qubit channels are studied under two broad classes: amplitude damping channels and generalized depolarizing channels. A canonical derivation of the Kraus representation of the former, via the Choi isomorphism is presented for the general case of a system's interaction with a squeezed thermal bath. This isomorphism is also used to characterize the difference in the geometry and rank of these channel classes. Under the isomorphism, the degree of decoherence is quantified according to the mixedness or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the former…
We study the geometric phase of an open two-level quantum system under the influence of a squeezed, thermal environment for both non-dissipative as well as dissipative system-environment interactions. In the non-dissipative case, squeezing is found to have a similar influence as temperature, of suppressing geometric phase, while in the dissipative case, squeezing tends to counteract the suppressive influence of temperature in certain regimes. Thus, an interesting feature that emerges from our work is the contrast in the interplay between squeezing and thermal effects in non-dissipative and dis…
We derive an upper limit for the mixedness of single bosonic mode gaussian states propagating in dissipative channels. It is a function of the initial squeezing and temperature of the channel only. Moreover the time at which von Neumann's entropy reaches its maximum value coincides with that of complete loss of coherence, thus defining a quantum-classical transition.
The observation of genuine quantum features of nano-mechanical motion is a key goal for both fundamental and applied quantum science. To this end, a promising approach is the stabilization of nonclassical features in the presence of dissipation, by means of the tunable coupling with a photonic environment. Here we present a scheme that combines dissipative squeezing with a mechanical nonlinearity to stabilize arbitrary approximations of (displaced) mechanical Fock state of any number. We consider an optomechanical system driven by three control lasers--at the cavity resonance and at the two me…
A nondegenerate two-photon Jaynes-Cummings model is investigated where the leakage of photon through the cavity is taken into account. The effect of cavity damping on the mean photon number, atomic populations, field statistics and both field and atomic squeezing is considered on the basis of master equation in dressed-state approximation for initial coherent fields and excited atom.
Dissipative generation of spin squeezing in the resolved vacuum Rabi splitting limit
JILA, University of Colorado and National Institute of Standards and Technology（科罗拉多大学与美国国家标准与技术研究院联合JILA研究所）；Department of Physics, University of Colorado（科罗拉多大学物理系）；Center for Theory of Quantum Matter, University of Colorado（科罗拉多大学量子物质理论中心）；T.C.M. Group, Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室TCM小组）；Institute of Physics（物理研究所）
Using the way of deriving infinitive sum representation of density operator as a solution to the master equation describing the amplitude dissipative channel by virtue of the entangled state representation, we show manifestly how the initial density operator of a single-mode squeezed vacuum state evolves into a definite mixed state which turns out to be a squeezed chaotic state with decreasing-squeezing. We investigate average photon number, photon statistics distributions for this state.
Evolutions of quantum noise, characterized by quadrature squeezing parameter and Fano factor, and of mixedness, quantified by quantum von Neumann and linear entropies, of a pumped dissipative non-linear oscillator are studied. The model can describe a signal mode interacting with a thermal reservoir in a parametrically pumped cavity with a Kerr non-linearity. It is discussed that the initial pure states, including coherent states, Fock states, and finite superpositions of coherent states evolve into the same steady mixed state as verified by the quantum relative entropy and the Bures metric. I…
We study the generation of spin-squeezing in arrays of long-lived dipoles subject to collective emission, coherent drive, elastic interactions, and spontaneous emission. Counter-intuitively, it is found that the introduction of spontaneous emission leads to an enhancement of the achievable spin-squeezing, relative to that which emerges in the steady-state of the purely collective dynamics for the same model parameters. This behavior is connected to the dynamical self-tuning of the system through a dissipative phase transition that is present in the collective system alone. Our findings will be…
Mesoscopic mechanical oscillators can be prepared in quantum states and coherently manipulated using the optomechanical interaction. This has recently been used to prepare squeezed mechanical states. However, the scheme used in these experiments relies on slow, dissipative evolution that destroys the system's memory of its initial state. In this paper we propose a protocol based on a sequence of four pulsed optomechanical interactions. In addition to being coherent, our scheme executes in a time much shorter than a mechanical period. We analyse applications in impulsive force sensing and prese…
We develop a quantum theory describing the input-output properties of Josephson traveling wave parametric amplifiers. This allows us to show how such a device can be used as a source of nonclassical radiation, and how dispersion engineering can be used to tailor gain profiles and squeezing spectra with attractive properties, ranging from genuinely broadband spectra to "squeezing combs" consisting of a number of discrete entangled quasimodes. The device's output field can be used to generate a multi-mode squeezed bath--a powerful resource for dissipative quantum state preparation. In particular…
Nonclassical states of macroscopic objects are promising for ultrasensitive metrology as well as testing quantum mechanics. In this work, we investigate dissipative mechanical quantum state engineering in an optically levitated nanodiamond. First, we study single-mode mechanical squeezed states by magnetically coupling the mechanical motion to a dressed three-level system provided by a Nitrogen-vacancy center in the nanoparticle. Quantum coherence between the dressed levels is created via microwave fields to induce a two-phonon transition, which results in mechanical squeezing. Remarkably, we …
Micro- and nanoscale optical or microwave cavities are used in a wide range of classical applications and quantum science experiments, ranging from precision measurements, laser technologies to quantum control of mechanical motion. The dissipative photon loss via absorption, present to some extent in any optical cavity, is known to introduce thermo-optical effects and thereby impose fundamental limits on precision measurements. Here, we theoretically and experimentally reveal that such dissipative photon absorption can result in quantum feedback via in-loop field detection of the absorbed opti…
The radiation-pressure interaction between one or more laser fields and a mechanical oscillator gives rise to a wide range of phenomena: from sideband cooling and backaction-evading measurements to pondermotive and mechanical squeezing to entanglement and motional sideband asymmetry. In many protocols, such as dissipative mechanical squeezing, multiple lasers are utilized, giving rise to periodically driven optomechanical systems. Here we show that in this case, Floquet dynamics can arise due to presence of Kerr-type nonlinearities, which are ubiqitious in optomechanical systems. Specifically,…
Many quantum state preparation methods rely on a combination of dissipative quantum state initialization, followed by unitary evolution to a desired target state. Here we demonstrate the usefulness of quantum measurement as an additional tool for quantum state preparation. Starting from a pure separable multipartite state, a control sequence, which includes rotation, spin squeezing via one-axis twisting, quantum measurement and post-selection, generates a highly entangled multipartite state, which we refer to as Projected Squeezed states (or PS states). Through an optimization method, we then …
Some non-classical properties such as squeezing, sub-Poissonian photon statistics or oscillations in photon-number distributions may survive longer in a phase-sensitive environment than in a phase-insensitive environment. We examine if entanglement, which is an inter-mode non-classical feature, can also survive longer in a phase-sensitive environment. Differently from the single-mode case, we find that making the environment phase-sensitive does not aid in prolonging entanglement.
We revisit the dissipative approach to producing and stabilizing spin-squeezed states of an ensemble of $N$ two-level systems, providing a detailed analysis of two surprising yet generic features of such protocols. The first is a macroscopic sensitivity of the steady state to whether $N$ is even or odd. We discuss how this effect can be avoided (if the goal is parity-insensitive squeezing), or could be exploited as a new kind of sensing modality to detect the addition or removal of a single spin. The second effect is an anomalous emergent long timescale and a "prethermalized" regime that occur…
We study a quantum harmonic oscillator linearly coupled through the position operator $\hat{q}$ to a first bath and through the momentum operator $\hat{p}$ to a second bath yielding an Ohmic-Drude dissipation. We analyse the oscillator's fluctuations as a function of the ratio between the strength of the two couplings, focusing in particular on the situation in which the two dissipative interactions are comparable. Analytic formulas are derived in the relevant regimes corresponding to the low temperature limit and when the Drude high frequency cutoff is much larger than all other frequencies. …
We propose a continuous-variable quantum sensing scheme, in which a harmonic oscillator is employed as the probe to estimate the parameters in the spectral density of a quantum reservoir, within a non-Markovian dynamical framework. It is revealed that the sensing sensitivity can be effectively boosted by (i) optimizing the weight of the momentum-position-type coupling in the whole probe-reservoir interaction Hamiltonian, (ii) the initial quantum squeezing resource provided by the probe, (iii) the noncanonical equilibration induced by the non-Markovian effect, and (iv) applying an external driv…
Dissipation is generally thought to affect the quantum nature of the system in an adverse manner, however we show that dissipatively coupled nano systems can be prepared in states which beat the standard quantum limit of the mechanical motion. We show that the reactive coupling between the waveguide and the microdisk resonator can generate the squeezing of the waveguide by injecting a quantum field and laser into the resonator through the waveguide. The waveguide can show about 70--75% of maximal squeezing for temperature about 1--10 mK. The maximum squeezing can be achieved with incident pump…
The strong light-matter coupling attainable in optical cavities enables the generation of highly squeezed states of atomic ensembles. It was shown in [Phys. Rev. A 66, 022314 (2002)] how an effective one-axis twisting Hamiltonian can be realized in a cavity setup. Here, we extend this work and show how an effective two-axis twisting Hamiltonian can be realized in a similar cavity setup. We compare the two schemes in order to characterize their advantages. In the absence of decoherence, the two-axis Hamiltonian leads to more squeezing than the one-axis Hamiltonian. If limited by decoherence fro…
Among the known resources of quantum metrology, one of the most practical and efficient is squeezing. Squeezed states of atoms and light improve the sensing of the phase, magnetic field, polarization, mechanical displacement. They promise to considerably increase signal-to-noise ratio in imaging and spectroscopy, and are already used in real-life gravitational-wave detectors. But despite being more robust than other states, they are still very fragile, which narrows the scope of their application. In particular, squeezed states are useless in measurements where the detection is inefficient or …
We study entanglement and squeezing of two uncoupled impurities immersed in a Bose-Einstein condensate. We treat them as two quantum Brownian particles interacting with a bath composed of the Bogoliubov modes of the condensate. The Langevin-like quantum stochastic equations derived exhibit memory effects. We study two scenarios: (i) In the absence of an external potential, we observe sudden death of entanglement; (ii) In the presence of an external harmonic potential, entanglement survives even at the asymptotic time limit. Our study considers experimentally tunable parameters.
We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via a quantum nondemoliton type of coupling, such that there is decoherence without dissipation, as well as when it interacts via a dissipative interaction, resulting in decoherence as well as dissipation. The system is taken to be either a two-level atom (or equivalently, a spin-1/2 system) or a harmonic oscillator, and the environment is modeled as a bath of …
Combination of dissipative and dispersive coupling in the cavity optomechanical systems
Faculty of Physics, M.V. Lomonosov Moscow State University（莫斯科国立大学物理系）；Quantum Technology Centre, M.V. Lomonosov Moscow State University（莫斯科国立大学量子技术中心）
We investigate the emergence of a time crystal in a driven-dissipative many-body spin array. In this system the interplay between incoherent spin pumping and collective emission stabilizes a synchronized non-equilibrium steady state which in the thermodynamic limit features a self-generated time-periodic pattern imposed by collective elastic interactions. In contrast to prior realizations where the time symmetry is already broken by an external drive, here it is only spontaneously broken by the elastic exchange interactions and manifest in the two-time correlation spectrum. Employing a combina…
