The notion of spin squeezing involves reduction in the uncertainty of a component of the spin vector below a certain limit. This aspect has been studied earlier for pure and mixed states of definite spin. In this paper, this study has been extended to coupled spin states which do not possess sharp spin value. A general squeezing criterion has been obtained by requiring that a direct product state for two spinors is not squeezed. The squeezing aspect of entangled states is studied in relation to their spin- spin correlations.
The celebrated Majorana representation is exploited to investigate spin squeezing in different classes of pure symmetric states of N qubits with two distinct spinors, namely the Dicke-class of states. On obtaining a general expression for spin squeezing parameter, the variation of squeezing for different configurations is studied in detail.It is shown that the states in the Dicke-class, characterized by two-distinct non-orthogonal spinors, exhibit squeezing.
Majorana geometric representation of pure N-qubit states obeying exchange symmetry is em- ployed to explore spin squeezing properties in the family of states with two distinct spinors. Dicke states are characterized by two orthogonal spinors and belong to this family - but they are not spin squeezed. On the otherhand, those constituted by two non-orthogonal spinors exhibit spin squeezing.
We propose a method for engineering spin dynamics in ensembles of integer-spin atoms confined within a high-finesse optical cavity. Our proposal uses cavity-assisted Raman transitions to engineer a Dicke model for integer-spin atoms, which, in a dispersive limit, reduces to effective atom-atom interactions within the ensemble. This scheme offers a promising and flexible new avenue for the exploration of a wide range of spinor many-body physics. As an example of this, we present results showing that this method can be used to generate spin-nematic squeezing in an ensemble of spin-1 atoms. With …
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…
The nature of spin squeezing has been studied earlier for a coupled state of two spinors by Usha Devi et. al. (J. Phys. A: Math. Gen. 36 5333 (2003)). In this paper, we extend this study to a coupled state of two spin-1 systems. Here, we show that the direct product of two spin-1 states exhibits squeezing unlike the direct product of two spinors. We investigate the nature of squeezing for non-separable coupled state of two spin-1 systems and identify the parameters which are responsible for the existence of squeezing. We also provide ways to generate them by external interactions.
We study the effect of dipolar interactions on the level of squeezing in spin-1 Bose-Einstein condensates by using the single mode approximation. We limit our consideration to the $\mathfrak{su}(2)$ Lie subalgebra spanned by spin operators. The biaxial nature of dipolar interactions allows for dynamical generation of spin-squeezed states in the system. We analyze the phase portraits in the reduced mean-filed space in order to determine positions of unstable fixed points. We calculate numerically spin squeezing parameter showing that it is possible to reach the strongest squeezing set by the tw…
We analyze quantum correlation properties of a spinor-1 (f=1) Bose Einstein condensate using the Gell-Mann realization of SU(3) symmetry. We show that previously discussed phenomena of condensate fragmentation and spin-mixing can be explained in terms of the hypercharge symmetry. The ground state of a spinor-1 condensate is found to be fragmented for ferromagnetic interactions. The notion of two bosonic mode squeezing is generalized to the two spin (U-V) squeezing within the SU(3) formalism. Spin squeezing in the isospin subspace (T) is found and numerically investigated. We also provide new r…
The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin 1/2 states and study its squeezing behaviour as a function of the individual polarizations of the two spinors.
Coherence has been remaining a key resource for numerous applications of quantum physics ranging from quantum metrology to quantum information. Here, we report a theoretical work on how maximally created coherence results in the squeezing of cavity field coupled to a coherently driven single quantum dot. We employ a recently developed polaron master equation theory for accurately incorporating the impact of exciton-phonon coupling on squeezing.
Spin squeezed states are a class of entangled states of spins that have practical applications to precision measurements. In recent years spin squeezing with one-axis twisting (OAT) has been demonstrated experimentally with spinor BECs with more than 10^3 atoms. Although the noise is below the standard quantum limit, the OAT scheme cannot reduce the noise down to the ultimate Heisenberg limit. Here we propose an experimentally feasible scheme based on optimized quantum control to greatly enhance the performance of OAT to approach the Heisenberg limit, requiring only an OAT Hamiltonian and the …
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.
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 …
We present a scheme for generating and manipulating three-mode squeezed states with genuine tripartite entanglement by injecting single-mode squeezed light into an array of coupled optical waveguides. We explore the possibility to selectively generate single-mode squeezing or multimode squeezing at the output of an elliptical waveguides array, determined solely by the input light polarization. We study the effect of losses in the waveguides array and show that quantum correlations and squeezing are preserved for realistic parameters. Our results show that arrays of optical waveguides are suita…
The realization of the strong coupling regime is requisite for implementing quantum information tasks. Here, a method for enhancing the atom-field coupling in highly dissipative coupled cavities is proposed. By introducing parametric squeezing into the primary cavity which is only virtually excited under specific parametric conditions, coupling enhancement between atom and auxiliary cavity is realized for proper squeezing parameters. This enables the system to be robust against large cavity decay and atomic spontaneous emission. The observation of vacuum Rabi oscillations show that the origina…
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…
We investigate the exact dynamics of a system of two independent harmonic oscillators coupled through their angular momentum. The exact analytic solution of the equations of motion for the field operators is derived, and the conditions for dynamical stability are obtained. As application, we examine the emergence of squeezing and mode entanglement for an arbitrary separable coherent initial state. It is shown that close to instability, the system develops considerable entanglement, which is accompanied with simultaneous squeezing in the coordinate of one oscillator and the momentum of the othe…
We propose an efficient method for controlled generation of field squeezing with cold atomic clouds trapped close to a superconducting transmission line resonator. It is shown that, based on the coherent strong magnetic coupling between the collective atomic spins and microwave fields in the transmission line resonator, two-mode or single mode field squeezed states can be generated through coherent control on the dynamics of the system. The degree of squeezing and preparing time can be directly controlled through tuning the external classical fields. This protocol may offer a promising platfor…
We observe that a weak guided light field transmitted through an ensemble of atoms coupled to an optical nanofiber exhibits quadrature squeezing. From the measured squeezing spectrum we gain direct access to the phase and amplitude of the energy-time entangled part of the two-photon wavefunction which arises from the strongly correlated transport of photons through the ensemble. For small atomic ensembles we observe a spectrum close to the lineshape of the atomic transition, while sidebands are observed for sufficiently large ensembles, in agreement with our theoretical predictions. Furthermor…
We study the effect of the intermode coupling in the generation of coherence when two bosonic modes are bilinearly coupled. We consider the case for which the two modes are weakly coupled and the rotating-wave approximation (RWA) applies and the case for which they are strongly coupled and the (RWA) does not apply. Then, in the regime of validity of (RWA), there is no coherence generation solely due to squeezing effects, which means there is an exchange of excitation between the modes and negligible squeezing. On the other hand, if the two modes are strongly coupled coherence is generated by t…
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…
We consider a small partially reflecting vibrating mirror coupled dispersively to a single optical mode of a high finesse cavity. We show this arrangement can be used to implement quantum squeezing of the mechanically oscillating mirror.
We consider a star network consisting of N oscillators coupled to a central one which in turn is coupled to an infinite set of oscillators (reservoir), which makes it leaking. Two of the N + 1 normal modes are dissipating, while the remaining N - 1 lie in a frequency range which is more and more squeezed as the coupling strengths increase, which realizes synchronization of the single parts of the system.
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…
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…
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 demonstrate continuous tuning of the squeezing level generated in a double-ring optical parametric oscillator by externally controlling the coupling condition using electrically controlled integrated microheaters. We accomplish this by utilizing the avoided crossing exhibited by a pair of coupled silicon nitride microring resonators. We directly detect a change in the squeezing level from 0.5 dB in the undercoupled regime to 2 dB in the overcoupled regime, which corresponds to a change in the generated on-chip squeezing factor from 0.9 dB to 3.9 dB. Such wide tunability in the squeezing lev…
We study the squeezing as well as the statistical properties of the output radiation from a degenerate parametric oscillator coupled to a squeezed vacuum reservoir employing the stochastic differential equations associated with the normal ordering. It is found that the degree of squeezing of the output radiation is less than the corresponding cavity radiation. However, for output radiation the correlation of the quadrature operators evaluated at different times also exhibits squeezing, which is the reason for quenching of the overall noise in one of the quadrature components of the squeezing s…
We evaluate the spin squeezing dynamics of N independent spin-1/2 particles with exchange symmetry. Each spin interacts with its own reservoir, and the reservoirs are independently and identical. The spin squeezing parameter is analytically calculated with different kinds of decoherence. The spin squeezing property vanishes with evolution time under the Markovian decoherence. Whereas coupled to the non-Markovian decoherence channels, the spin squeezing property collapses and revives with time. As spin squeezing can be regarded as a witness of multipartite entanglement, thus our scheme shows th…
We study the limitations to the relative number squeezing between photons and atoms coupled out from a homogeneous Bose-Einstein-Condensate. We consider the coupling between the translational atomic states by two photon Bragg processes, with one of the photon modes involved in the Bragg process in a coherent state, and the other initially unpopulated. We start with an interacting Bose- condensate at zero temperature and compute the time evolution for the system. We study the squeezing, i.e. the variance of the occupation number difference between the second photon and the atomic c.m. mode. We …
We study the spin squeezing property of weighted graph states, which can be used to improve the sensitivity in interferometry. Decoherence reduces the spin squeezing property but the result remains superior over other reference schemes with GHZ-type maximally entangled states and product states. We study the time evolution of spin squeezing of weighted graph states coupled to different decoherence channels. Based on the analysis, the spin squeezing of the weighted graph states is robust in the presence of decoherence and the decoherence limit in the improvement of the interferometric sensitivi…
In a driven atom-cavity coupled system in which the two-level atom is driven by a classical field, the cavity mode which should be in a coherent state in the absence of its reservoir, can be squeezed by coupling to its reservoir. The squeezing effect is enhanced as the damping rate of the cavity is increased to some extent.
Investigations of spin squeezing in ensembles of quantum particles have been limited primarily to a subspace of spin fluctuations and a single spatial mode in high-spin and spatially extended ensembles. Here, we show that a wider range of spin-squeezing is attainable in ensembles of high-spin atoms, characterized by sub-quantum-limited fluctuations in several independent planes of spin-fluctuation observables. Further, considering the quantum dynamics of an $f=1$ ferromagnetic spinor Bose-Einstein condensate, we demonstrate theoretically that a high degree of spin squeezing is attained in mult…
Advances in the emerging field of coherent quantum feedback control (CQFC) have led to the development of new capabilities in the areas of quantum control and quantum engineering, with a particular impact on the theory and applications of quantum optical networks. We consider a CQFC network consisting of two coupled optical parametric oscillators (OPOs) and study the squeezing spectrum of its output field. The performance of this network as a squeezed-light source with desired spectral characteristics is optimized by searching over the space of model parameters with experimentally motivated bo…
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 demonstrate a novel dual-beam atom laser formed by outcoupling oppositely polarized components of an F=1 spinor Bose-Einstein condensate whose Zeeman sublevel populations have been coherently evolved through spin dynamics. The condensate is formed through all-optical means using a single-beam running-wave dipole trap. We create a condensate in the field-insensitive $m_F=0$ state, and drive coherent spin-mixing evolution through adiabatic compression of the initially weak trap. Such dual beams, number-correlated through the angular momentum-conserving reaction $2m_0\leftrightharpoons m_{+1}+…
We propose a potentially practical scheme for realization of two-mode squeezed state with respect to two distant nitrogen-vacancy center ensembles coupled to two interconnected mechanical modes of diamond nanoresonators. By making use of the tunable phonon-spin interaction and the engineered phonon-phonon tunneling, both the desired excitation transfer process and the optimal two-mode squeezing between spin ensembles can be realized. We investigate the dynamics of the total system under infulences from the mechanical decay using both analytical and numerical methods, where the realistic condit…
We propose a simple method for generating spin squeezing of atomic ensembles in a Floquet cavity subject to a weak, detuned two-photon driving. We demonstrate that {\it the weak squeezing of light inside the cavity can, counterintuitively, induce strong spin squeezing}. This is achieved by exploiting the anti-Stokes scattering process of a photon pair interacting with an atom. Specifically, {\it one photon of the photon pair is scattered into the cavity resonance by absorbing partially the energy of the other photon whose remaining energy excites the atom}. The scattering, combined with a Floq…
We study a system of two nanomechanical resonators embedded in a dc SQUID. We show that the inductively-coupled resonators can be treated as two entangled quantum memory elements with states that can be read from, or written on by employing the SQUID as a displacement detector or switching additional external magnetic fields, respectively. We present a scheme to squeeze the even modeof the state of the resonators and consequently reduce the noise in the measurement of the magnetic flux threading the SQUID. Wefinally analyze the effect of dissipation on the squeezing using the quantum master eq…
Spin squeezing inequalities (SSI) represent a major tool to probe quantum entanglement among a collection of few-level atoms, and are based on collective spin measurements and their fluctuations. Yet, for atomic ensembles of spin-$j$ atoms and ultracold spinor gases, many experiments can image the populations in all Zeeman sublevels $s=-j, -j+1, \dots, j$, potentially revealing finer features of quantum entanglement not captured by SSI. Here we present a systematic approach which exploits Zeeman-sublevel population measurements in order to construct novel entanglement criteria, and illustrate …
Parametric amplification of quantum fluctuations constitutes a fundamental mechanism for spontaneous symmetry breaking. In our experiments, a spinor condensate acts as a parametric amplifier of spin modes, resulting in a twofold spontaneous breaking of spatial and spin symmetry in the amplified clouds. Our experiments permit a precise analysis of the amplification in specific spatial Bessel-like modes, allowing for the detailed understanding of the double symmetry breaking. On resonances that create vortex-antivortex superpositions, we show that the cylindrical spatial symmetry is spontaneousl…
We investigate the generation of photon-phonon entangled states by exploiting stimulated Brillouin scattering in nanoscale waveguides. The squeezing type Hamiltonian that represents creation and annihilation of photon-phonon pairs is obtained out of the multimode photon-phonon interaction Hamiltonian in the presence of a pump field. The Bogoliubov eigenstates of the Hamiltonian, which are a coherent mix of propagating photons and phonons, show squeezing properties in the uncertainties of the collective quadrature operators. The measurement of the photonic component can provide a controllable s…
We predict that exploiting spin-orbit coupling in a harmonically trapped spinor quantum gas can lead to scaling of the optimal measurement precision beyond the Heisenberg scaling. We show that quadratic scaling with the number of atoms can be facilitated via squeezed center-of-mass excitations of the atomic motion using a 1D spin-orbit coupled fermions or strongly interacting bosons (Tonks-Girardeau gas). Based on predictions derived from analytic calculations of the corresponding quantum Fisher information, we then introduce a protocol which overcomes the Heisenberg scaling (and limit) with h…
It has been shown elsewhere that two spatially separated atoms can jointly absorb one photon, whose frequency is equal to the sum of the transition frequencies of the two atoms. We describe this process in the presence of an ensemble of many two-level atoms, and show that it can be used to generate spin squeezing and entanglement. This resonant collective process allows to create a sizeable squeezing already at the single-photon limit. It represents a novel way for generating manybody spin-spin interactions, yielding a two-axis twisting-like interaction among the spins, which is very effcient …
We present a scheme allowing to access the squeezing parameter of multimode fields by means of the dynamics of nonlocal quantum probes. The model under consideration is composed of two two-level systems which are coupled locally to an environment consisting of nonlocally correlated field modes given by two-mode Gaussian states. Introducing independently switchable interactions, one observes revivals of nonlocal coherences of the two-qubit system which are unambiguously connected to the squeezing parameter of the Gaussian environmental states. Thus, the locally interacting two two-level systems…
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 …
Quantum spin squeezing is an important resource for quantum information processing, but its squeezing degree is not easy to preserve in an open system with decoherence. Here, we propose a scheme to implement single-photon-triggered spin squeezing with decoherence reduction in an open system. In our system, a Dicke model (DM) is introduced into the quadratic optomechanics, which can be equivalent to an effective DM manipulated by the photon number. Besides, the phonon mode of the optomechanical system is coupled to a squeezed vacuum reservoir with a phase matching, resulting in that the thermal…
We observe spin squeezing in three-component Bose gases where all three hyperfine states are coupled by synthetic spin-orbit coupling. This phenomenon is a direct consequence of spin-orbit coupling, as can be seen clearly from an effective spin Hamiltonian. By solving this effective model analytically with the aid of a Holstein-Primakoff transformation for spin-1 system in the low excitation limit, we conclude that the spin-nematic squeezing, a novel category of spin squeezing existing exclusively in large spin systems, is enhanced with increasing spin-orbit intensity and effective Zeeman fiel…
