Entanglement plays a crucial role in proposals for quantum metrology, yet demonstrating quantum enhancement in sensing with sustained spin entanglement remains a challenging endeavor. Here, we combine optical pumping and continuous quantum nondemolition measurements to achieve a sustained spin squeezed state with $\bm{4 \times 10^{10}}$ hot atoms. A metrologically relevant steady state squeezing of $\bm{-3.23 \pm 0.24}$ dB using prediction and retrodiction is maintained for about one day. We employ the system to track different types of continuous time-fluctuating magnetic fields, where we construct deep learning models to decode the measurement records from the optical signals. Quantum enhancement due to the steady spin squeezing is verified in our atomic magnetometer. These results represent important progress towards applying long-lived quantum entanglement resources in realistic settings.
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 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.
We present a scheme to generate steady-state atomic spin squeezing in a cavity QED system using cavity-mediated Raman transitions to engineer effective atom-photon interactions, which include both linear and nonlinear (dispersive) atom-cavity couplings, on a potentially equal footing. We focus on a regime where the dispersive coupling is very large and find that the steady state of the system can in fact be a strongly spin-squeezed Dicke state, $|N/2,0\rangle$, of the atomic ensemble. These states offer Heisenberg-limited metrological properties and feature genuine multipartite entanglement am…
We study the physical properties of double-cavity optomechanical system in which the mechanical resonator interacts with one of the coupled cavities and another cavity is used as an auxiliary cavity. The model can be expected to achieve the strong optomechanical coupling strength and overcome the optomechanical cavity decay, simultaneously. Through the coherent auxiliary cavity interferences, the steady-state squeezing of mechanical resonator can be generated in highly unresolved sideband regime. The validity of the scheme is assessed by numerical simulation and theoretical analysis of the ste…
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…
Triplet down conversion, the process of converting one high-energy photon into three low-energy photons, may soon be experimentally feasible due to advances in optical resonator technology. We use quantum phase-space techniques to analyse the process of degenerate intracavity triplet down conversion by solving stochastic differential equations within the truncated positive-P representation. The time evolution of both intracavity mode populations are simulated, and the resulting steady-states are examined as a function of the pump intensity. Quantum effects are most pronounced in the region imm…
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…
Nonlinear forces allow motion of a mechanical oscillator to be squeezed below the zero-point motion. Of existing methods, mechanical parametric amplification is relatively accessible, but previously thought to be limited to 3dB of squeezing in the steady state. We consider the effect of applying continuous weak measurement and feedback to this system. If the parametric drive is optimally detuned from resonance, correlations between the quadratures of motion allow unlimited steady-state squeezing. Compared to back-action evasion, we demonstrate that the measurement strength, temperature and eff…
Quantum squeezing in mechanical systems is not only a key signature of macroscopic quantum effects, but can also be utilized to advance the metrology of weak forces. Here we show that strong mechanical squeezing in the steady state can be generated in an optomechanical system with mechanical nonlinearity and red-detuned monochromatic driving on the cavity mode. The squeezing is achieved as the joint effect of nonlinearity-induced parametric amplification and cavity cooling, and is robust against thermal fluctuations of the mechanical mode.
The generated magnitude of quadrature squeezing in a cavity-coupled ensemble, which is continuously driven using a coherent off-axis field, is theoretically explored. Using a truncated set of equations-of-motion derived from a Dicke Hamiltonian, steady-state quadrature squeezing of the cavity field is numerically calculated to approach a limit of -3 dB, while frequency-modulated quadrature squeezing approaches a limit of -14 dB, in the absence of pure-dephasing, and as a function of the ensemble's size and detuning. The impact of pure-dephasing on steady-state quadrature squeezing is shown to …
Tracking a randomly varying optical phase is a key task in metrology, with applications in optical communication. The best precision for optical phase tracking has till now been limited by the quantum vacuum fluctuations of coherent light. Here we surpass this coherent-state limit by using a continuous-wave beam in a phase-squeezed quantum state. Unlike in previous squeezing-enhanced metrology, restricted to phases with very small variation, the best tracking precision (for a fixed light intensity) is achieved for a finite degree of squeezing, due to Heisenberg's uncertainty principle. By opti…
With the purpose of controlling the steady state of a dielectric nanosphere levitated within an optical cavity, we study its conditional dynamics under simultaneous sideband cooling and additional time-continuous measurement of either the output cavity mode or the nanosphere's position. We find that the average phonon number, purity and quantum squeezing of the steady-states can all be made more non-classical through the addition of time-continuous measurement. We predict that the continuous monitoring of the system, together with Markovian feedback, allows one to stabilize the dynamics for an…
In the absence of decay, the conditional dynamics for an opensystem is often describable by a non-Hermitian Hamiltonian. This study investigates spin squeezing (SS) in non-Hermitian one-axis twisting (OAT) model. Somewhat surprisingly, SS close to the limit of Hermitian two-axis counter twisting (TACT) Hamiltonian is achievable for some parameters, which significantly improves upon the optimal value realizable by Hermitian OAT model. The drawback is like with all conditional schemes, it takes on average longer time to evolve into steady state, and the probability of no decay or success decreas…
We show that a squeezed bath, that acts on the central element of a harmonic chain, can drive the whole system to a steady state featuring a series of nested entangled pairs of oscillators that, ideally, covers the whole chain regardless of its size. We study how to realize this effect in various physical implementations, including optomechanical and superconducting devices, using currently available technologies. In these cases no squeezed fields are actually needed, and the squeezed bath is, instead, simulated by quantum reservoir engineering with bichromatic drives.
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.
In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric non…
We discuss how large amounts of steady-state quantum squeezing (beyond 3 dB) of a mechanical resonator can be obtained by driving an optomechanical cavity with two control lasers with differing amplitudes. The scheme does not rely on any explicit measurement or feedback, nor does it simply involve a modulation of an optical spring constant. Instead, it uses a dissipative mechanism with the driven cavity acting as an engineered reservoir. It can equivalently be viewed as a coherent feedback process, obtained by minimally perturbing the quantum nondemolition measurement of a single mechanical qu…
The interaction of classical and quantized electromagnetic fields with an ensemble of atoms in an optical cavity is considered. Four fields drive a double-lambda level scheme in the atoms, consisting of a pair of lambda systems sharing the same set of lower levels. Two of the fields produce maximum coherence, rho12 = -1/2, between the ground state sublevels 1 and 2. This pumping scheme involves equal intensity fields that are resonant with both the one and two-photon transitions of the lambda system. There is no steady-state absorption of these fields, implying that the fields induce a type el…
We show that high squeezing and entanglement can be generated at the output of a cavity containing atoms interacting with two fields in a Coherent Population Trapping situation, on account of a non-linear Faraday effect experienced by the fields close to a dark-state resonance in a cavity. Moreover, the cavity provides a feedback mechanism allowing to reduce the quantum fluctuations of the ground state spin, resulting in strong steady state spin-squeezing.
We propose an experimentally feasible method for enhancing the atom-field coupling as well as the ratio between this coupling and dissipation (i.e., cooperativity) of two atoms in an optical cavity. Our method also enables the generation of steady-state nearly-maximal quantum entanglement. Our approach exploits optical parametric amplification to exponentially enhance the atom-cavity interaction and, hence, the cooperativity of the system, with the squeezing-induced fluctuation noise being completely eliminated. Thus, an effective cooperativity much larger than $100$ can be achieved even for m…
We study the quantum critical effect enhanced spin-nematic squeezing and quantum Fisher information (QFI) in the spin-1 dipolar atomic Bose-Einstein condensate. We show that the quantum phase transitions can improve the squeezing and QFI in the nearby regime of critical point, and the Heisenberg-limited high-precision metrology can be obtained. The different properties of the ground squeezing and entanglement under even and odd number of atoms are further analyzed, by calculating the exact analytical expressions.We also demonstrate the squeezing and entanglement generated by the spin-mixing dy…
We consider a wide family of optical coherent feedback loops acting on an optomechanical system operating in the linearized regime. We assess the efficacy of such loops in improving key operations, such as cooling, steady-state squeezing and entanglement, as well as optical to mechanical state transfer. We find that mechanical sideband cooling can be enhanced through passive, interferometric coherent feedback, achieving lower steady-state occupancies and considerably speeding up the cooling process; we also quantify the detrimental effect of non-zero delay times on the cooling performance. Ste…
We propose a scheme for the generation of a two-mode field squeezed state in cavity QED. It is based on two-channel Raman excitations of a beam of three-level atoms with random arrival times by two classical fields and two high-Q resonator modes. It is shown that by suitably choosing the intensities and detunings of fields the dynamical processes can be selective and two-mode squeezing between the cavity modes can be generated at steady state. This proposal does not need the preparation of the initial states of atoms and cavity modes, and is robust against atomic spontaneous decay.
We develop a general framework to describe interferometric coherent feedback loops and prove that, under any such scheme, the steady-state squeezing of a bosonic mode subject to a rotating wave coupling with a white noise environment and to any quadratic Hamiltonian must abide by a noise-dependent bound that reduces to the 3dB limit at zero temperature. Such a finding is contrasted, at fixed dynamical parameters, with the performance of homodyne continuous monitoring of the output modes. The latter allows one to beat coherent feedback and the 3dB limit under certain dynamical conditions, which…
We show that the robust spin squeezing preservation can be achieved by utilizing detuning modification for an ensemble of N separate two-level atoms embedded in photonic crystal cavities (PCC). In particular, we explore the different dynamical behaviors of spin squeezing between isotropic and anisotropic PCC cases when the atomic frequency is inside the band gap. In both cases, it is shown that the robust preservation of spin squeezing is completely determined by the formation of bound states. Intriguingly, we find that unlike the isotropic case where steady-state spin squeezing varies smoothl…
Spin squeezing of an ensemble of N atoms in a high-Q cavity is shown to be enhanced by continuous measurement of photons in the cavity. A degree of spin squeezing proportional to N^{-1/3} is attained as a quasi-steady state over a broad set of initial states of the atoms and photons.
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…
We explore the effects of quantum mechanical squeezing on the nonequilibrium fluctuations of bosonic transport between two squeezed harmonic reservoirs and a two level system. A standard full counting statistics technique based on a quantum master equation is employed. We derive a nonzero thermodynamic affinity under equal temperature setting of the two squeezed reservoirs. The odd cumulants are shown to be independent of squeezing under symmetric conditions, whereas the even cumulants depend nonlinearly on the squeezing parameters. The odd and even cumulants saturate at two different but uniq…
While the squeezing of a propagating field can, in principle, be made arbitrarily strong, the cavity-field squeezing is subject to the well-known 3 dB limit, and thus has limited applications. Here, we propose the use of a fully quantum degenerate parametric amplifier (DPA) to beat this squeezing limit. Specifically, we show that by {\it simply} applying a two-tone driving to the signal mode, the pump mode can, {\it counterintuitively}, be driven by the photon loss of the signal mode into a squeezed steady state with, in principle, an {\it arbitrarily high} degree of squeezing. Furthermore, we…
Quantum correlations in the steady state of light-emitter ensembles from perturbation theory
Univ Lyon, Ens de Lyon, CNRS, Laboratoire de Physique（里昂大学、巴黎高等师范学校里昂分校、法国国家科学研究中心、物理实验室）；Advanced Concepts Team, European Space Agency, European Space Research and Technology Centre（欧洲航天局先进概念团队、欧洲空间研究和技术中心）
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…
The output field from a continuously driven linear parametric oscillator may exhibit considerably more squeezing than the intracavity field. Inspired by this fact, we explore the nonclassical features of the steady-state output field of a driven nonlinear Kerr parametric oscillator using a temporal wave packet mode description. Utilizing a new numerical method, we have access to the density matrix of arbitrary wave packet modes. Remarkably, we find that even though the steady-state cavity field is always characterized by a positive Wigner function, the output may exhibit Wigner negativity, dep…
It is generally believed that dispersive polarimetric detection of collective angular momentum in large atomic spin systems gives rise to: squeezing in the measured observable, anti-squeezing in a conjugate observable, and collective spin eigenstates in the long-time limit (provided that decoherence is suitably controlled). We show that such behavior only holds when the particles in the ensemble cannot be spatially distinguished-- even in principle-- regardless of whether the measurement is only sensitive to collective observables. While measuring a cloud of spatially-distinguishable spin-1/2 …
We derive and evaluate equations of motion for the mean values and variances of the components of spins collectively coupled to a broadband squeezed radiation reservoir. Our formalism bridges between a single two-level emitter, represented by spin components that relax at different rates, depending on the degree of squeezing, to an ensemble of emitters represented by a large collective spin, whose components relax independently of the squeezing. For a single spin, the steady state fluctuations in the transverse components are independent of the squeezing, while the steady state of a large spin…
Dissipation-driven quantum state engineering uses the environment to steer the state of quantum systems and preserve quantum coherence in the steady state. We show that modulating the damping rate of a microwave resonator generates a vacuum squeezed state of arbitrary squeezing strength, thereby constituting a mechanism allowing perfect squeezing. Given the recent experimental realizations in circuit QED of a microwave resonator with a tunable damping rate [Yin et al., Phys. Rev. Lett. 110, 107001 (2013)], superconducting circuits are an ideal playground to implement this technique. By dispers…
We propose an approach for collective enhancement of precision for remotely located optical lattice clocks and a way of generation of the Einstein-Podolsky-Rosen state of remote clocks. Close to Heisenberg scaling of the clock precision with the number of clocks M can be achieved even for an optical channel connecting clocks with substantial losses. This scenario utilizes a collective quantum nondemolition measurement on clocks with parallel Bloch vectors for enhanced measurement precision. We provide an optimal network solution for distant clocks as well as for clocks positioned in close prox…
Hybrid architectures integrating mesoscopic electronic conductors with resonant microwave cavities have a great potential for investigating unexplored regimes of electron-photon coupling. In this context, producing nonclassical squeezed light is a key step towards quantum communication with scalable solid-state devices. Here we show that parametric driving of the electronic conductor induces a squeezed steady state in the cavity. We find that squeezing properties of the cavity are essentially determined by the electronic noise correlators of the quantum conductor. In the case of a tunnel junct…
High-order quantum correlations in nonlinear waveguide quantum electrodynamics
Academia Sinica（中央研究院）；National Central University（中央大学）；University of Mataram（马塔兰大学）；National Center for Theoretical Sciences（国家理论科学中心）；Hon Hai Research Institute（鸿海研究院）；National Taiwan University（台湾大学）
It is desirable to observe synchronization of quantum systems in the quantum regime, defined by low number of excitations and a highly non-classical steady state of the self-sustained oscillator. Several existing proposals of observing synchronization in the quantum regime suffer from the fact that the noise statistics overwhelms synchronization in this regime. Here we resolve this issue by driving a self-sustained oscillator with a squeezing Hamiltonian instead of a harmonic drive and analyze this system in the classical and quantum regime. We demonstrate that strong entrainment is possible f…
We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is non-thermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output …
We investigate steady-state thermal transport and photon statistics in a nonequilibrium hybrid quantum system, in which a qubit is longitudinally and quadratically coupled to an optical resonator. Our calculations are conducted with the method of the quantum dressed master equation combined with full counting statistics. The effect of negative differential thermal conductance is unravelled at finite temperature bias, which stems from the suppression of cyclic heat transitions and large mismatch of two squeezed photon modes at weak and strong qubit-resonator hybridizations, respectively. The gi…
When two chains of quantum systems are driven at their ends by a two-mode squeezed reservoir, they approach a steady state characterized by the formation of many entangled pairs. Each pair is made of one element of the first and one of the second chain. This effect has been already predicted under the assumption of broadband squeezing. Here we investigate the situation of finite-bandwidth reservoirs. This is done by modeling the driving bath as the output field of a non-degenerate parametric oscillator. The resulting non-Markovian dynamics is studied within the theoretical framework of cascade…
Levitated particles are a promising platform for precision sensing of external perturbations and probing the boundary between quantum and classical worlds. A critical obstacle for these applications is the difficulty of generating nonclassical states of motion which have not been realized so far. Here, we show that strong squeezing of the motion of a levitated particle below the vacuum level is feasible with available experimental parameters. Using suitable modulation of the trapping potential (which is impossible with clamped mechanical resonators) and coherent scattering of trapping photons …
We propose an efficient scheme for generating spin-squeezed states at steady state in a spin-mechanical hybrid system, where an ensemble of SiV centers are coupled to a strongly damped nanomechanical resonator. We show that,there exists a collective steady state in the system, which is exactly formed by the collective spin states plus the zero excitation state of the mechanical mode. The generation of the steady spin-squeezed state is based on a dissipative quantum dynamical process in which the mechanical dissipation plays a positive role but without destroying the target state. We demonstrat…
We investigate theoretically the properties of squeezed states generated using degenerate parametric down conversion in lossy cavities. We show that the Lindblad master equation, which governs the evolution of this system, has as its solution a squeezed thermal state with an effective temperature and squeezing parameter that depends on time. We derive analytical solutions for the time-evolution of quadrature noise, thermal photon number, squeezing parameter, and total photon number under different pumping regimes. We also find the steady state limits of the quadrature noises and discuss the $ …
