Spin Squeezing Research Articles

Spin squeezing in a spin-orbit-coupled Bose-Einstein condensate

We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as $^{87}$Rb and $^{23}$Na in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.

Exploring entropic uncertainty relation and dense coding capacity in a two-qubit X-state

The measurement precision for two incompatible observables in a typical quantum system can be improved by the aid of one particle as a quantum memory. In this work, we study the entropic uncertainty relation in the presence of quantum memory (EUR-QM) and dense coding capacity (DCC) for arbitrary two-qubit X-states, and then we obtain an explicit relationship between the lower bound of the uncertainty and DCC. As an example, we examine the thermal EUR-QM as well as DCC in two kinds of two-qubit spin squeezing models (one-axis twisting model and two-axis counter-twisting model) under an external magnetic field. In the following, we relate EUR-QM to DCC and show analytically that there is an anti-correlated relation between them, and especially in the ground state. Our results show that for both the models, the entropic uncertainty and its bound can be decreased by reinforcing the spin squeezing parameters or decreasing the temperature of the system. Notably, we reveal that the valid dense coding cannot carry out in the one-axis twisting model, nevertheless, if we properly choose the Hamiltonian parameters, the two-axis counter-twisting model not only carries out the valid dense coding but also the optimal dense coding surely can be achieved. Thereby, our observations might offer new insights into quantum measurement precision and the optimal dense coding for the regimes of various solid-state systems.

Generation of atomic spin squeezing via quantum coherence: Heisenberg–Langevin approach

Taking into account the dephasing process in the realistic atomic ensemble, we theoretically study the generation of atomic spin squeezing via atomic coherence induced by the coupling and probe fields. Using the Heisenberg–Langevin approach, we find that the perfect spin squeezing in the X component can be obtained while the coupling and probe fields produce the maximum coherence between the ground state sublevels 1 and 2. Moreover, the degree of atomic spin squeezing in the X component can be strengthened with the increasing atomic density and/or Rabi frequency of the mixing field. The theoretical results provide a proof-of-principle demonstration of generating the atomic spin squeezing via quantum coherence in the realistic atomic ensemble which may find potential applications in quantum information processing and quantum networks.

Producing and storing spin-squeezed states and Greenberger-Horne-Zeilinger states in a one-dimensional optical lattice

Dynamical generation and storage of spin-squeezed states in few-body cold-atom systems within one-dimensional optical lattices are investigated theoretically through an exact diagonalization approach. The structure of the Mott-squeezed states is revealed by correlation functions on-site and between different sites.

Retrieval of cavity-generated atomic spin squeezing after free-space release

The compatibility of cavity-generated spin-squeezed atomic states with atom-interferometric sensors that require freely falling atoms is demonstrated. An ensemble of $500,000$ spin-squeezed atoms in a high-finesse optical cavity with near-uniform atom-cavity coupling is prepared, released into free space, recaptured in the cavity, and probed. Up to $\sim$10 dB of metrologically-relevant squeezing is retrieved for 700 microsecond free-fall times, and decaying levels of squeezing are realized for up to 3 millisecond free-fall times. The degradation of squeezing results from loss of atom-cavity coupling homogeneity between the initial squeezed state generation and final collective state read-out. A theoretical model is developed to quantify this degradation and this model is experimentally validated.

Free Space Ramsey Spectroscopy in Rubidium with Noise below the Quantum Projection Limit.

We demonstrate the utility of optical cavity generated spin-squeezed states in free space atomic fountain clocks in ensembles of 390 000 ^{87}Rb atoms. Fluorescence imaging, correlated to an initial quantum nondemolition measurement, is used for population spectroscopy after the atoms are released from a confining lattice. For a free fall time of 4milliseconds, we resolve a single-shot phase sensitivity of 814(61) microradians, which is 5.8(0.6) decibels (dB) below the quantum projection limit. We observe that this squeezing is preserved as the cloud expands to a roughly 200 μm radius and falls roughly 300 μm in free space. Ramsey spectroscopy with 240 000 atoms at a 3.6ms Ramsey time results in a single-shot fractional frequency stability of 8.4(0.2)×10^{-12}, 3.8(0.2)dB below the quantum projection limit. The sensitivity and stability are limited by the technical noise in the fluorescence detection protocol and the microwave system, respectively.

Relating spin squeezing to multipartite entanglement criteria for particles and modes

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 connection to widely-used entanglement criteria that depend on the state's polarization. Our results are relevant for state-of-the-art experiments where symmetric entangled states are distributed into a number of addressable modes, such as split spin-squeezed Bose-Einstein condensates.

Squeezing metrology: a unified framework

Quantum metrology theory has up to now focused on the resolution gains obtainable thanks to the entanglement among N probes. Typically, a quadratic gain in resolution is achievable, going from the 1/N of the central limit theorem to the 1/N of the Heisenberg bound. Here we focus instead on quantum squeezing and provide a unified framework for metrology with squeezing, showing that, similarly, one can generally attain a quadratic gain when comparing the resolution achievable by a squeezed probe to the best N-probe classical strategy achievable with the same energy. Namely, here we give a quantification of the Heisenberg squeezing bound for arbitrary estimation strategies that employ squeezing. Our theory recovers known results (e.g. in quantum optics and spin squeezing), but it uses the general theory of squeezing and holds for arbitrary quantum systems.

Probing dynamical phase transitions with a superconducting quantum simulator.

Nonequilibrium quantum many-body systems, which are difficult to study via classical computation, have attracted wide interest. Quantum simulation can provide insights into these problems. Here, using a programmable quantum simulator with 16 all-to-all connected superconducting qubits, we investigate the dynamical phase transition in the Lipkin-Meshkov-Glick model with a quenched transverse field. Clear signatures of dynamical phase transitions, merging different concepts of dynamical criticality, are observed by measuring the nonequilibrium order parameter, nonlocal correlations, and the Loschmidt echo. Moreover, near the dynamical critical point, we obtain a spin squeezing of -7.0 ± 0.8 dB, showing multipartite entanglement, useful for measurements with precision fivefold beyond the standard quantum limit. On the basis of the capability of entangling qubits simultaneously and the accurate single-shot readout of multiqubit states, this superconducting quantum simulator can be used to study other problems in nonequilibrium quantum many-body systems, such as thermalization, many-body localization, and emergent phenomena in periodically driven systems.

Entanglement and Spin Squeezing in the Evolution of a Resonant Field in a Kell-Like Medium

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.

Enhancing the sensitivity of an atom interferometer to the Heisenberg limit using increased quantum noise

In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1 / N . Under usual spin squeezing, the sensitivity is increased by lowering the quantum noise. It is also possible to increase the sensitivity by leaving the quantum noise unchanged while producing phase amplification. Here we show how to increase the sensitivity, to the Heisenberg limit of 1 / N , while increasing the quantum noise by N and amplifying the phase by a factor of N . Because of the enhancement of the quantum noise and the large phase magnification, the effect of excess noise is highly suppressed. The protocol uses a Schrödinger cat state representing a maximally entangled superposition of two collective states of N atoms. The phase magnification occurs when we use either atomic state detection or collective state detection; however, the robustness against excess noise occurs only when atomic state detection is employed. We show that for one version of the protocol, the signal amplitude is N when N is even, and is vanishingly small when N is odd, for both types of detection. We also show how the protocol can be modified to reverse the nature of the signal for odd versus even values of N . Thus, for a situation where the probability of N being even or odd is equal, the net sensitivity is within a factor of 2 of the Heisenberg limit. Finally, we discuss potential experimental constraints for implementing this scheme via one-axis-twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed because of the increased quantum noise and the large phase magnification inherent to the protocol. As a result, we find that the maximum improvement in sensitivity can be close to the ideal limit for as many as 10 million atoms.

Spin squeezing of 1011 atoms by prediction and retrodiction measurements.

The measurement sensitivity of quantum probes using N uncorrelated particles is restricted by the standard quantum limit1, which is proportional to [Formula: see text]. This limit, however, can be overcome by exploiting quantum entangled states, such as spin-squeezed states2. Here we report the measurement-based generation of a quantum state that exceeds the standard quantum limit for probing the collective spin of 1011 rubidium atoms contained in a macroscopic vapour cell. The state is prepared and verified by sequences of stroboscopic quantum non-demolition (QND) measurements. We then apply the theory of past quantum states3,4 to obtain spin state information from the outcomes of both earlier and later QND measurements. Rather than establishing a physically squeezed state in the laboratory, the past quantum state represents the combined system information from these prediction and retrodiction measurements. This information is equivalent to a noise reduction of 5.6 decibels and a metrologically relevant squeezing of 4.5 decibels relative to the coherent spin state. The past quantum state yields tighter constraints on the spin component than those obtained by conventional QND measurements. Our measurement uses 1,000 times more atoms than previous squeezing experiments5-10, with a corresponding angular variance of the squeezed collective spin of 4.6×10-13 radians squared. Although this work is rooted in the foundational theory of quantum measurements, it may find practical use in quantum metrology and quantum parameter estimation, as we demonstrate by applying our protocol to quantum enhanced atomic magnetometry.

Spin squeezing by one-photon–two-atom excitation processes in atomic ensembles

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 for the generation of spin squeezing. We perform explicit calculations for ensembles of magnetic molecules coupled to a superconducting coplanar cavities. This system represents an attractive on-chip architecture for the realization of improved sensing.

Super dense coding in one-axis twisting model

We study thermal dense coding in a two-spin model under an external magnetic eld. Its depen-dencies on magnetic eld, strength of the spin squeezing and temperature are presented in detail.Our main goal now is to study how we can increase the thermal dense coding capacity in the presenceof magnetic eld, strength of the spin squeezing and temperature. It shows that the dense codingtend to valid value by setting the value of the input quantum correlations. Our most importantmotive for this study is to examine the relationship between the thermal properties of super quan-tum discord (SQD) and dense coding. The results show that the thermal properties of the SQD onour channel enable us to determine when and under what conditions the system is suitable for validdense coding. Our proposals could be lead to that this scheme is efficient for quantum informationprocessing.

Generation of Nonclassical State via Two-Axis Counter Twisting Interactions

We investigate the generation of nonclassical state via two-axis counter twisting interactions. By the bosonization method, we analytically and numerically calculate the spin squeezing parameter and the entanglement parameter. Its shows that the strength of the nonlinear interaction and the orientation of spin squeezing play important role in generating nonclassical states.

Steady-State Spin Squeezing Generated in Diamond Nanostructures Coupled to Carbon Nanotubes

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.

Persistent spin squeezing of a dissipative one-axis twisting model embedded in a general thermal environment

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 memory time.

Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas.

We report on the realization of long-range Ising interactions in a cold gas of cesium atoms by Rydberg dressing. The interactions are enhanced by coupling to Rydberg states in the vicinity of a Förster resonance. We characterize the interactions by measuring the mean-field shift of the clock transition via Ramsey spectroscopy, observing one-axis twisting dynamics. We furthermore emulate a transverse-field Ising model by periodic application of a microwave field and detect dynamical signatures of the paramagnetic-ferromagnetic phase transition. Our results highlight the power of optical addressing for achieving local and dynamical control of interactions, enabling prospects ranging from investigating Floquet quantum criticality to producing tunable-range spin squeezing.

Short-time expansion of Heisenberg operators in open collective quantum spin systems

We present a new method to compute short-time expectation values in large collective spin systems with generic Markovian decoherence. Our method is based on a Taylor expansion of a formal solution to the equations of motion for Heisenberg operators. This expansion can be truncated at finite order to obtain virtually exact results at short times that are relevant for metrological applications such as spin squeezing. In order to evaluate the expansion for Heisenberg operators, we compute the relevant structure constants of a collective spin operator algebra. We demonstrate the utility of our method by computing spin squeezing, two-time correlation functions, and out-of-time-ordered correlators for $10^4$ spins in strong-decoherence regimes that are otherwise inaccessible via existing numerical methods. Our method can be straightforwardly generalized to the case of a collective spin coupled to bosonic modes, relevant for trapped ion and cavity QED experiments, and may be used to investigate short-time signatures of quantum chaos and information scrambling.

Spin Squeezing Base on Four Wave Mixing

We investigate how to prepare spin squeezing state base on four wave mixing. By the bosonization method, we analytically and numerically calculate the spin squeezing parameter. Spin squeezed state can be periodically or always prepared for two different cases. The better squeezing can be achieved by increasing the total number of photons and decreasing the. frequency difference.