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In this study, we explore the ground state phase diagram of the spin-1/2 XX chain model, which features X Z Y - Y Z X -type three-spin interactions (TSIs). This model, while seemingly simple, reveals a rich tapestry of quantum behaviors. Our analysis relies on several key metrics. The ' l 1 -norm of coherence' helps us identify coherent states within the phase diagram, which represent states capable of superposition and interference. We employ the 'spin squeezing parameter' to pinpoint unique coherent states characterized by isotropic noise in all directions, making them invaluable for quantum metrology. Additionally, we utilize the 'entanglement entropy' to determine which of these coherent states exhibit entanglement, indicating states that cannot be fully described by local variables. Our research unveils diverse regions within the phase diagram, each characterized by coherent, squeezed, or entangled states, offering insights into the quantum phenomena underling these systems. We also study the critical scaling versus the system size for the mentioned quantities. [ABSTRACT FROM AUTHOR]

Atomic nonlinear interferometry has wide applications in quantum metrology and quantum information science. Here we propose a nonlinear time-reversal interferometry scheme with high robustness and metrological gain based on the spin squeezing generated by arbitrary quadratic collective-spin interaction, which could be described by the Lipkin–Meshkov–Glick (LMG) model. We optimize the squeezing process, encoding process, and anti-squeezing process, finding that the two particular cases of the LMG model, one-axis twisting and two-axis twisting outperform in robustness and precision, respectively. Moreover, we propose a Floquet driving method to realize equivalent time reverse in the atomic system, which leads to high performance in precision, robustness, and operability. Our study sets a benchmark for achieving high precision and high robustness in atomic nonlinear interferometry. [ABSTRACT FROM AUTHOR]

The atomic squeezing in a system of M two level atoms interacting with a coherent radiation of single mode is analyzed. The time dependent squeezing factor S has been calculated and the impact of the photons number and other parameters are studied. I considered approximation that mean numbers of photons are small in comparison to number of atoms. Small atomic squeezing is obtained under the approximation. One may obtain larger squeezing by increasing the mean number of photons. I plotted the graph for time evaluation of squeezing factor for different value of photons and fixed value of atoms presented in different atomic states. [ABSTRACT FROM AUTHOR]

In this study, we analyzed the properties of entanglement in the ground state of an N -qubit cluster. For the first time, we discussed the previously overlooked relation between spin squeezing and concurrence for a multi-qubit system, and critically explained the special value of parameter at which the concurrence becomes 0. Additionally, this work also elaborates on the relation between decay probability and concurrence for the multiple numbers of qubits. Results showed that when the number of qubits is high, the decay is sharp as compared to the small number of qubits, which indicates that entanglement dies faster at a higher number of qubits. [ABSTRACT FROM AUTHOR]

We show that the lowest quantum Cramér-Rao bound achievable in interferometry with a one-axis twisted spin coherent state is saturated by the asymptotic method of moments error of a protocol that uses one call to the one-axis twisting, one call to time-reversed one-axis twisting, and a final total spin measurement (i.e., a twist-untwist protocol). The result is derived by first showing that the metrological phase diagram for one-axis twisting is asymptotically characterized by a single quantum Fisher information value N ( N + 1)/2 for all times, then constructing a twist-untwist protocol having a method of moments error that saturates this value. The case of finite-range one-axis twisting is similarly analyzed, and a simple functional form for the metrological phase diagram is found in both the short-range and long-range interaction regimes. Numerical evidence suggests that the finite-range analogues of twist-untwist protocols can exhibit a method of moments error that asymptotically saturates the lowest quantum Cramér-Rao bound achievable in interferometry with finite-range one-axis twisted spin coherent states for all interaction times.

In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.

We propose a Rydberg molecule dressing scheme to create strong and long-ranged interactions at selective distances. This is achieved through laser coupling ground-state atoms off-resonantly to an attractive molecular curve of two interacting Rydberg atoms. Although dephasing due to Rydberg state decay occurs in all dressing schemes, an advantage of the molecule dressing is that a large ratio of dressed interaction to dephasing rate can be realized at large atomic separations. In an optical lattice or tweezer setting, we show that the strong interaction permits the fast generation of spin squeezing for several tens of dressed atoms. The proposed setting offers a new route to study complex many-body dynamics and to realize quantum information processing with non-convex long-range interactions. [ABSTRACT FROM AUTHOR]

We propose a scheme to generate photon–phonon entanglement and spin squeezing in a hybrid system which is composed of the nitrogen–vacancy (NV) centers, nanomechanical resonator (NMR), and optical cavity. The triplet ground states of the NV centers which have been embedded in the middle of the clamped–clamped NMR are dressed by two strong microwave fields. Kerr nonlinearity is established by an applied microwave field and the vibrational modes of NMR coupling to the dressed-state transitions. The quantum correlations of the applied microwave field, vibrational mode, and NV centers are realized based on the parametric down-conversion-like and beam-splitter-like interactions in the hybrid system, which generate the photon–phonon entanglement and spin squeezing. In this nonlinear processes, the dynamically mediated strain of NMR, as a nonlinear switch, plays the central role in the establishment of such quantum correlations. Our scheme can be applied to quantum nondemolition measurement, quantum sensing, and quantum metrology. • Photon–phonon entanglement and spin squeezing are established based on parametric down-conversion-like and beam-splitter-like interactions. • In the existed schemes based on NV centers, the triplet ground states were just dressed partially, and simplified to the two-level system. In our scheme, we study in the dressed picture and found quantum correlations. • Our scheme can be applied to quantum nondemolition measurement, quantum sensing, and quantum metrology. [ABSTRACT FROM AUTHOR]

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 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, 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 Floquet sideband, provides an alternative mechanism to implement Heisenberg-limited spin squeezing. Our proposal does not need multiple classical and cavity-photon drivings applied to atoms in ensembles, and therefore its experimental feasibility is greatly improved compared to other cavity-based schemes. As an example, we demonstrate a possible implementation with a superconducting resonator coupled to a nitrogen-vacancy electronic-spin ensemble.

Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve practical quantum advantage over classical computers. Here, we explore variational quantum algorithms, with different levels of qubit connectivity, for digital simulation of the ground state of long-range interacting systems as well as generation of spin squeezed states. We find that as the interaction becomes more long-ranged, the variational algorithms become less efficient, achieving lower fidelity and demanding more optimization iterations. In particular, when the system is near its criticality the efficiency is even lower. Increasing the connectivity between distant qubits improves the results, even with less quantum and classical resources. Our results show that by mixing circuit layers with different levels of connectivity one can sensibly improve the performance. Interestingly, the order of layers becomes very important and grouping the layers with long-distance connectivity at the beginning of the circuit outperforms other permutations. The same design of circuits can also be used to variationally produce spin squeezed states, as a resource for quantum metrology.

Collective spin operators for symmetric multi-quDit (namely identical D-level atom) systems generate a U(D) symmetry. We explore generalizations to arbitrary D of SU(2)-spin coherent states and their adaptation to parity (multi-component Schrödinger cats), together with multi-mode extensions of NOON states. We write level, one- and two-quDit reduced density matrices of symmetric N-quDit states, expressed in the last two cases in terms of collective U(D)-spin operator expectation values. Then, we evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies of the corresponding reduced density matrices. In particular, we analyze the numerical and variational ground state of Lipkin–Meshkov–Glick models of 3-level identical atoms. We also propose an extension of the concept of SU(2)-spin squeezing to SU(D) and relate it to pairwise D-level atom entanglement. Squeezing parameters and entanglement entropies are good markers that characterize the different quantum phases, and their corresponding critical points, that take place in these interacting D-level atom models. [ABSTRACT FROM AUTHOR]

We investigate spin squeezing in Bose–Einstein condensate with three-body interaction. By using the short-time approximation, we analytically and numerically calculate the spin squeezing parameter. Its shown that increased squeezing can be achieved by increasing the number of atoms, two- and three-body interactions and Josephson-like coupling. Its also shown that three-body interaction causes increased squeezing than two-body interaction. [ABSTRACT FROM AUTHOR]

We propose to take advantage of the very weak coupling of the ground-state helium-3 nuclear spin to its environment to produce very long-lived macroscopic quantumstates, here nuclear spin squeezed states, in a gas cell at roomtemperature. To performa quantumnon-demolitionmeasurement of a transverse component of the previously polarized collective nuclear spin, a discharge is temporarily switched on in the gas, which populates helium-3 metastable state. The collective spin corresponding to the F Æ 1/2 metastable level then hybridizes slightly with the one in the ground state by metastability exchange collisions. To access the nuclear spin fluctuations, one continuously measures the light field leaking out of an optical cavity, where it has interacted dispersively with the metastable state collective spin. In a model of three coupled collective spins (nuclear, metastable and Stokes for light) in the Primakoff approximation, and for two measurement schemes, we calculate the moments of the collective nuclear spin squeezed component Iz conditioned on the optical signal averaged over the observation time t. In the photon counting scheme, we find that the squeezed observable is I 2 z rather than Iz. In the homodyne detection scheme, we analytically solve the stochastic equation for the state of the system conditioned to the measurement; the conditional expectation value of Iz depends linearly on the signal and the conditional variance of Iz does not depend on it. The conditional variance decreases as (¡sqt)¡1, where the squeezing rate ¡sq, which we calculate explicitly, depends linearly on the light intensity in the cavity at weak atom-field coupling and saturates at strong coupling to the ground state metastability exchange effective rate, proportional to the metastable atom density. Finally, we take into account the de-excitation of metastable atoms at the walls, which induces nuclear spin decoherence with an effective rate °®. It imposes a limit / (°®/¡sq)1/2 on the conditional variance reached in a time / (°®¡sq)¡1/2. A multilingual version is available on the open archive HAL at https://hal.archives-ouvertes.fr/hal-03083577. [ABSTRACT FROM AUTHOR]

We investigate spin squeezing of a Bose-Einstein condensate in an open symmetrical double-well trap with dissipation in the tunneling process, which can be treated as a tunneling-dissipative Bose-Hubbard dimer. Perturbation technique based on the system is applied. Its shown that more squeezing can be achieved by increasing the tunneling rate and the dissipation. [ABSTRACT FROM AUTHOR]

We investigate entanglement and spin squeezing in the evolution of a resonant field in a Kell-like medium. With perturbation techniques, we first obtain the approximate analytical solution of the wave function, and then we further analytically and numerically calculate two mode entangled parameter and spin squeezing parameter. Its shows that the stronger entanglement and more squeezing may be achieved by increasing the coupling strength. [ABSTRACT FROM AUTHOR]

An experimentally feasible scheme for preparing the squeezed spin states in a novel spin–mechanical hybrid system is studied. The setup under consideration is realized by a single‐crystal diamond waveguide with negatively charged silicon‐vacancy (SiV) centers embedded. After studying the strain couplings between the SiV spins and the propagating phonon modes, analyses show that long‐range spin–spin interactions can be achieved under large detuning condition. Modeled as an effective one‐axis twisting Hamiltonian, these nonlinear spin–spin couplings can steer the system to the squeezed spin states in the practical situations. This proposal may have interesting applications in high‐precision metrology and quantum information processing. [ABSTRACT FROM AUTHOR]

Spin squeezed state, as an important quantum resource, can be used to implement the high precise measurement beyond the standard quantum limit. Based on the recent novel scheme that strong magnetomechanical interaction between a single Nitrogen-vacancy (NV) spin and the vibrational mode of the suspended nanotube is engineered (Li et al. Phys. Rev. Lett. 117, 015502 2016), we investigate the steady-state spin squeezing behaviors of a spin ensemble in diamond coupled to carbon nanotubes by exerting a controllable microwave field. We show that steady-state spin squeezing can be generated with the help of the microwave field, despite the damping from mechanical damping. This investigation based on spin-spin interaction in diamond might apply to magnetometers, interferometry, and other precision measurement measurements. [ABSTRACT FROM AUTHOR]

We in this paper investigate the spin squeezing in relation with the phase transition from the normal to superradiant phases for two atoms in an optical cavity. The squeezing vanishes in the normal phase and jumps sharply to the maximum bound above the critical point of phase transition. In the high atom-field coupling regime, the squeezing vanishes again when the atom-field coupling reaches a threshold value. The squeezing alternates between two spin components in the intermediate region of atom-field coupling. An interesting observation is that the two spin components are squeezed alternately with the variation of phase angle of the cavity field. The squeezing factor indeed can be used to probe the phase transition and coherent-field properties as well. [ABSTRACT FROM AUTHOR]

We investigate spin squeezing of the generalized one-axis twisting model. By using the perturbation techniques, we analytically and numerically calculate spin squeezing parameter defined by Kitagawa and Ueda. It shows that more squeezing may be achieved by strengthening linear interactions and increasing the total number of particles. [ABSTRACT FROM AUTHOR]

We study the evolution of a Bose–Einstein condensate in a two-state superposition due to inter-state interactions. Using a population imbalanced dynamic decoupling scheme, we measure inter-state interactions while canceling intra-state density shifts and external noise sources. Our measurements show low statistical uncertainties for both magnetic sensitive and insensitive superpositions, indicating that we successfully decoupled our system from strong magnetic noises. We experimentally show that the Bloch sphere representing general superposition states is ‘twisted’ by inter-state interactions, as predicted in [ 1 , 2 ] and the twist rate depends on the difference between inter-state and intra-state scattering lengths a _22 + a _11 − 2 a _12 . We use the non-linear spin dynamics to demonstrate squeezing of Gaussian noise, showing 2.79 ± 0.43 dB squeezing when starting with a noisy state and applying 160 echo pulses, which can be used to increase sensitivity when there are errors in state preparation. Our results allow for a better understanding of inter-atomic potentials in ^87 Rb. Our scheme can be used for spin-squeezing beyond the standard quantum limit and observing polaron physics close to Feshbach resonances, where interactions diverge, and strong magnetic noises are ever present.

Wedescribe an experiment where spin squeezing occurs spontaneously within a standard Ramsey sequence driving a two-component Bose--Einstein condensate (BEC) of87Rb atoms trapped in an elongated magnetic trap. The squeezing is generated by state-dependent collisional interactions, despite the near-identical scattering lengths of the spin states in 87Rb. In our proof-of-principle experiment, we observe a metrological spin squeezing that reaches 1.3 ± 0.4 dB for 5000 atoms, with a contrast of 90 ± 1%. The method may be applied to realize spin-squeezed BEC sources for atom interferometry without the need for cavities, state-dependent potentials or Feshbach resonances. [ABSTRACT FROM AUTHOR]

Recently proposed quantum-chaotic sensors achieve quantum enhancements in measurement precision by applying nonlinear control pulses to the dynamics of the quantum sensor while using classical initial states that are easy to prepare. Here, we use the cross-entropy method of reinforcement learning (RL) to optimize the strength and position of control pulses. Compared to the quantum-chaotic sensors with periodic control pulses in the presence of superradiant damping, we find that decoherence can be fought even better and measurement precision can be enhanced further by optimizing the control. In some examples, we find enhancements in sensitivity by more than an order of magnitude. By visualizing the evolution of the quantum state, the mechanism exploited by the RL method is identified as a kind of spin-squeezing strategy that is adapted to the superradiant damping.

We propose and analyze a realizable scheme for performing a Heisenberg-limited Mach–Zehnder interferometry with a dipolar spin-1 condensate. Based upon adiabatic processes of sweeping the transverse magnetic field, we demonstrate a perfect phase transition, which accomplishes the beam splitter, phase shifter and recombiner as for a Mach–Zehnder interferometer. The attractive dipolar interaction ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. We also study the spin squeezing of the state generated in the beam splitter and show that the spin squeezing exhibits an extremum near the critical point of phase transition. [ABSTRACT FROM AUTHOR]

We investigate spin squeezing and entanglement of the two-axis twisting model with the bosonization method, The smaller linear interaction can produce a stronger spin squeezing, the better entanglement and the squeezing and entanglement can maintain a longer time interval. The stronger spin squeezing and the better entanglement can also be achieved by increasing the number of particles. [ABSTRACT FROM AUTHOR]

We investigate spin squeezing of the one-axis twisting model. By using short-time approximation solutions of the angular momentum operators, we analytically and numerically calculate the spin squeezing parameter. It is shown that smaller linear interaction can produce a stronger spin squeezing and maintain a longer time interval. It is also shown that the stronger spin squeezing can be achieved by increasing the number of particles. [ABSTRACT FROM AUTHOR]

We study quantum entanglement and spin squeezing in multiparticle conversion system. It shown that entanglement and spin squeezing can be generated rapidly in the dynamical process and maintained in a long time interval; and the stronger squeezing and the better entanglement cab be achieved by increasing the total number of the particles. [ABSTRACT FROM AUTHOR]

We investigate spin squeezing (SS) and the quantum Fisher information (QFI) for the Jaynes-Cummings-Dicke (JCD) model in a two-component atomic Bose-Einstein condensate (BEC) inside an optical cavity. Analytical expressions for spin squeezing and the reciprocal of the quantum Fisher information per particle (RMQFI) are derived using the frozen spin approximation. It is shown that in the superradiant phase near the critical point, maximum squeezing and maximum quantum entanglement occur and thus the critical point emerges as a useful resource for precision measurements. In the presence of decoherence and particle loss, we show that gradually with time, even though the ability of squeezing and entanglement generation are weakened, yet significant amounts are still present which can be relevant to quantum information processing and precision spectroscopy. [ABSTRACT FROM AUTHOR]

We investigate quantum entanglement and spin squeezing of two species Bose-Einstein condensates. By the rotating-wave approximation, we obtain the effective Hamiltonian and the wave function of the system. It's shown that more entanglement and squeezing may be achieved by increasing the population difference of particles. [ABSTRACT FROM AUTHOR]

We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N = 2 to N = 100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations among the N atoms. [ABSTRACT FROM AUTHOR]

As the quantum states of nitrogen vacancy (NV) center can be coherently manipulated and obtained at room temperature, it is important to generate steady-state spin squeezing in spin qubits associated with NV impurities in diamond. With this task we consider a new type of a hybrid magneto-nano-electromechanical resonator, the functionality of which is based on a magnetic-field induced deflection of an appropriate cantilever that oscillates between NV spins in diamond. We show that there is bistability and spin squeezing state due to the presence of the microwave field, despite the damping from mechanical damping. Moreover, we find that bistability and spin squeezing can be controlled by the microwave field and the parameter V z . Our scheme may have the potential application on spin clocks, magnetometers, and other measurements based on spin–spin system in diamond nanostructures. [ABSTRACT FROM AUTHOR]

We investigate quantum entanglement in a generic-spin model with spin squeezing criterions based on squeezing inequalities. By analytically and numerically calculating the squeezing criterions, we show that the system is always entangled except at some special times and the stronger entanglement may be achieved by decreasing the coupling strength and increasing the number of particles. [ABSTRACT FROM AUTHOR]

We investiage Local Unitary Invariant Spin Squeezing (LUISS) in symmetric and non-symmetric multiqubit states. On developing an operational procedure to evaluate Local Unitary Invariant Spin Squeezing parameters, we explicitly evaluate these parameters for pure as well as mixed non-symmetric multiqubit states. We show that the existence of local unitary invariant version of Kitegawa-Ueda spin squeezing may not witness pairwise entanglement whereas the local unitary invariant analogue of Wineland spin squeezing necessarily implies pairwise entanglement. [ABSTRACT FROM AUTHOR]

We investigate coherence and squeezing of a two-mode Bose-Einstein condensate trapped in a double-well potential. By analytically deriving the form of coherence and numerically calculating the squeezing parameter, we show that the coherence and the squeezing may be controlled by adjusting some parameters of the two-mode Bose-Einstein condensate. [ABSTRACT FROM AUTHOR]

We present a theoretical scheme for generating spin squeezed state of atom-photon in atomic Bose-Einstein condensate(BEC) via electromagnetically induced transparency(EIT). Here we focus on the influence of the laser-atom dipole interaction and the two-photon detuning on the degree of spin squeezing. The stronger laser-atom dipole interaction and the smaller two-photon detuning more rapidly induces the stronger spin squeezing. [ABSTRACT FROM AUTHOR]

Spin squeezing is a form of entanglement that can improve the stability of quantum sensors operating with multiple particles, by inducing inter-particle correlations that redistribute the quantum projection noise. Previous analyses of potential metrological gain when using spin squeezing were performed on theoretically ideal states, without incorporating experimental imperfections or inherent limitations which result in non-unitary quantum state evolution. Here, we show that potential gains in clock stability are substantially reduced when the spin squeezing is non-unitary, and derive analytic formulas for the clock performance as a function of squeezing, excess spin noise, and interferometer contrast. Our results highlight the importance of creating and employing nearly pure entangled states for improving atomic clocks.

We investigate entanglement dynamics in Lipkin model, where the entanglement properties are characterized by witness operator and spin squeezing parameter. We first obtain operator solutions under the frozen-spin approximation and then calculate witness operator and spin squeezing parameter. They show that the entangled state can be generated and its degree of entanglement can be controlled by adjusting the weight of the one-particle number operator and the weight of the interaction. [ABSTRACT FROM AUTHOR]