We determine the complete set of generalized spin squeezing inequalities. These are entanglement criteria that can be used for the experimental detection of entanglement in a system of spin-1/2 particles in which the spins cannot be individually addressed. They can also be used to show the presence of bound entanglement in the thermal states of several spin models.
What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components J_k. They can be used for the experimental detection of entanglement in a system of spin-1/2 particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of: (i) the mean values and variances of…
By identifying non-local effects in systems of identical Bosonic qubits through correlations of their commuting observables, we show that entanglement is not necessary to violate certain squeezing inequalities that hold for distinguishable qubits and that spin squeezing may not be necessary to achieve sub-shot noise accuracies in ultra-cold atom interferometry.
Particle number fluctuations, no matter how small, are present in experimental set-ups. One should rigorously take these fluctuations into account, especially, for entanglement detection. In this context, we generalize the spin squeezing inequalities introduced by Tóth et al. in Phys. Rev. Lett. 99, 250405 (2007). These new inequalities are fulfilled by all separable states even when the number of particle is not constant, and may present quantum fluctuations. These inequalities are useful for detecting entanglement in many-body systems when the super-selection rule does not apply, or when onl…
We introduce a multi-mode squeezing coefficient to characterize entanglement in $N$-partite continuous-variable systems. The coefficient relates to the squeezing of collective observables in the $2N$-dimensional phase space and can be readily extracted from the covariance matrix. Simple extensions further permit to reveal entanglement within specific partitions of a multipartite system. Applications with nonlinear observables allow for the detection of non-Gaussian entanglement.
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 analyze theoretically a scheme that produces spin squeezing via the continuous swapping of atom-photon entanglement into atom-atom entanglement, and propose an explicit experimental system where the necessary atom-field coupling can be realized. This scheme is found to be robust against perturbations due to other atom-field coupling channels.
Entanglement witnesses based on first and second moments exist in the form of spin-squeezing criteria for the detection of particle entanglement from collective measurements, and in form of modified uncertainty relations for the detection of mode entanglement or steering. By revealing a correspondence between them, we show that metrologically useful spin squeezing reveals multimode entanglement in symmetric spin states that are distributed into addressable modes. We further derive tight state-independent multipartite entanglement bounds on the spin-squeezing coefficient and point out their con…
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…
A single four-level atom interacting with two-mode cavities is investigated. Under large detuning condition, we obtain the effective Hamiltonian which is unitary squeezing operator of two-mode fields. Employing the input-output theory, we find that the entanglement and squeezing of the output fields can be achieved. By analyzing the squeezing spectrum, we show that asymmetric detuning and asymmetric atomic initial state split the squeezing spectrum from one valley into two minimum values, and appropriate leakage of the cavity is needed for obtaining output entangled fields.
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 investigate the generation of the entanglement in a cavity magnomechanical system, which consists of three modes: a magnon mode, a microwave cavity mode and a mechanical vibration mode, the couplings of the magnon-photon and the magnon-phonon are achieved by the magnetic dipole interaction and the magnetostrictive interaction, respectively. By introducing a squeezing of the magnon mode, the magnon-photon and the magnon-phonon entanglements are significantly enhanced compared with the case without inserting the magnon squeezing. We find that an optimal parameter of the squeezing exists, whic…
We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement.
Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement…
We examine transfer of particle entanglement and spin squeezing between atomic and photonic subsystems in optical cavities coupled by two-photon exchange. Each cavity contains a single atom, interacting with cavity photons with a two-photon cascade transition. Particle entanglement is characterized by evaluating optimal spin squeezing inequalities, for the cases of initially separable and entangled two-photon states. It is found that particle entanglement is first generated among the photons in separate cavities and then transferred to the atoms. The underlying mechanism is recognized as an in…
Quantum entanglement reflects itself through non-local correlations among the subsystems of a quantum system. This thesis focuses on constructing a complete set of local invariants characterizing symmetric two qubit systems and analyzing the pairwise entanglement properties like collective spin squeezing - exhibited by multiqubits - in terms of two qubit entanglement invariants. Further, the collective pairwise entanglement properties of symmetric multiqubit states are shown to be captured entirely by the off diagonal block of the covariance matrix.
We apply spin-squeezing techniques to identify and quantify highly multi-partite photonic entanglement in polarization-squeezed light. We consider a practical single-mode scenario, and find that Wineland-criterion polarization squeezing implies entanglement of a macroscopic fraction of the total photons. A Glauber-theory computation of the observable N-photon density matrix, with N up to 100, finds that N-partite entanglement is observable despite losses and without post-selection. We estimate that existing detectors could observe $\sim1000$-partite entanglement from a few dB of polarization s…
A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A method for mapping the spin-squeezing inequalities for spin-1/2 particles to entanglement conditions for spin-j particles is also presented. We apply our mapping to obtain a generalization of the original spin-squeezing inequality to higher spins. We show that, for large particle numbers, a spin-squeezing parameter for entanglement detection based on one of our …
We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson-Schrödinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects…
We provide an in-depth characterization of a three modes Bose-Einstein condensate trapped in a symmetric circular triple well potential. We analyze how a subsystem independent measure of entanglement, the purity related to the su(3) algebra, scales for increasing number of atoms and signals correctly the quantum phase transition between two dynamical regimes in a specific arrangement. Moreover, this measure, which is intrinsically related to particle entanglement, also depicts if some squeezing is occurring when we consider the system's ground state.
We show that spin squeezing implies entanglement for quantum tripartite-state, where the subsystem of the bipartite-state is identical. We study the relation between spin squeezing parameters and entanglement through the quantum entropy of a system starts initially in a pure state when the cavity is binomial. We show that spin squeezing can be a convenient tool to give some insight into the subsystems entanglement dynamics when the bipartite subsystem interacts simultaneously with the cavity field subsystem, specially when the interaction occurs off-resonantly without and with a nonlinear medi…
We investigate nonlinear effects in an electromechanical system consisting of a superconducting charge qubit coupled to transmission line resonator and a nanomechanical oscillator, which in turn is coupled to another transmission line resonator. The nonlinearities induced by the superconducting qubit and the optomechanical coupling play an important role in creating optomechanical entanglement as well as the squeezing of the transmitted microwave field. We show that strong squeezing of the microwave field and robust optomechanical entanglement can be achieved in the presence of moderate therma…
We show that non-Hermitian dynamics generate substantial entanglement in many-body systems. We consider the non-Hermitian Lipkin-Meshkov-Glick model and show that its phase transition occurs with maximum multiparticle entanglement: there is full N-particle entanglement at the transition, in contrast to the Hermitian case. The non-Hermitian model also exhibits more spin squeezing than the Hermitian model, showing that non-Hermitian dynamics are useful for quantum metrology. Experimental implementations with trapped ions and cavity QED are discussed.
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…
The dispersive interaction of atoms and a far-detuned light field allows nondestructive imaging of the density oscillations in Bose-Einstein condensates. Starting from a ground state condensate, we investigate how the measurement back action leads to squeezing and entanglement of the quantized density oscillations. In particular, we show that properly timed, stroboscopic imaging and feedback can be used to selectively address specific eigenmodes and avoid excitation of non-targeted modes of the system.
We investigate the generation of squeezing and entanglement for the motional degrees of freedom of ions in linear traps, confined by time-varying and oscillating potentials, comprised of an DC and an AC component. We show that high degrees of squeezing and entanglement can be obtained by controlling either the DC or the AC trapping component (or both), and by exploiting transient dynamics in regions where the ions' motion is unstable, without any added optical control. Furthermore, we investigate the time-scales over which the potentials should be switched in order for the manipulations to be …
Quantum entanglement is a crucial resource for a wide variety of quantum technologies. However, the current state-of-art methods to generate quantum entanglement in optomechanical systems are not as efficient as all-optical methods utilizing nonlinear crystals. This article proposes a new scheme in which two single-mode squeezed light fields are injected into an optomechanical cavity. We demonstrate through our numerical simulations that the quantum entanglement can be substantially enhanced with the careful selection of squeezing strength and squeezing angle of the two quadrature squeezed lig…
We extend the criteria for $k$-particle entanglement from the spin squeezing parameter presented in [A.S. Sørensen and K. Mølmer, Phys. Rev. Lett. {\bf 86}, 4431 (2001)] to systems with a fluctating number of particles. We also discuss how other spin squeezing inequalities can be generalized to this situation. Further, we give an operational meaning to the bounds for cases where the individual particles cannot be addressed. As a by-product, this allows us to show that in spin squeezing experiments with cold gases the particles are typically distinguishable in practise. Our results justify the …
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…
Entanglement and squeezing in a two-mode system: theory and experiment
本文报道了在光学谐振腔中，线偏振光束与冷铯原子云相互作用产生不可分离光束。我们将两个线性偏振模式的压缩转换为正交纠缠，并展示了如何使用连续变量的不可分离性准则来找出双模系统中产生的最佳纠缠[Duan et al.，物理修订信函84，2722（2000）]。我们验证了这种方法的实验与直接测量的不可分性，使用两个零差检测。然后将这种纠缠映射到一个偏振基上，实现了偏振纠缠。
We propose a scheme to generate entanglement between two cavity modes and squeeze magnon mode in a magnon-cavity QED system, where the two microwave cavity modes are coupled with a massive yttrium iron garnet (YIG) sphere through magnetic dipole interaction. The nonlinearity used in our system originates from a squeezed driving via parametric down-conversion process, which is the reason to cause entanglement and squeezing. By using the mean field approximation and employing experimentally feasible parameters, we demonstrate that the system shows zero entanglement and squeezing without squeezed…
We introduce an entanglement-depth criterion optimized for planar quantum squeezed (PQS) states. It is connected with the sensitivity of such states for estimating an arbitrary, not necessarily small phase. We compare numerically our criterion with the well-known extreme spin squeezing condition of Sørensen and Mølmer [Phys. Rev. Lett. 86, 4431 (2001)] and show that our condition detects a higher depth of entanglement when both planar spin variances are squeezed below the standard quantum limit. We employ our theory to monitor the entanglement dynamics in a PQS state produced via quantum non-d…
In this paper, we study the interaction between a moving $Λ$-type three-level atom and a single-mode cavity field in the presence of intensity-dependent atom-field coupling. After obtaining the state vector of the entire system explicitly, we study the nonclassical features of the system such as quantum entanglement, position-momentum entropic squeezing, quadrature squeezing and sub-Poissonian statistics. According to the obtained numerical results we illustrate that the squeezed period, the duration of entropy squeezing and the maximal squeezing can be controlled by choosing the appropriate n…
Spectral components of continuous squeezed fields are entangled. In this article we review and clarify this phenomenon by analyzing systematically the relations between the correlations of modes filtered from stationary continuous fields and the cross power spectrum between the operators of the corresponding spectral components. Moreover, we study the specific spectral components that are filtered in homodyne or heterodyne detections and their entanglement properties. In particular, we establish the equivalence between two-mode squeezing variance and logarithmic negativity for the spectral com…
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially non-degenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of OAM modes is mapped on an orbital Poincare sphere, and the modes position on the sphere is spanned by the three orbital parameters. Using the non-degenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincare sphere…
