arXiv subjects
Publications and source records attributed to Alice Sinatra.
We show that, at finite temperature, the maximum spin squeezing achievable using interactions in Bose-Einstein condensates has a finite limit when the atom number $N\to \infty$ at fixed density and interaction strength. We calculate the limit of the squeezing parameter for a spatially homogeneous system and show that it is bounded from above by the initial non-condensed fraction.
The problem of spin squeezing with a bimodal condensate in presence of particle losses is solved analytically by the Monte Carlo wavefunction method. We find the largest obtainable spin squeezing as a function of the one-body loss rate, the two-body and three-body rate constants, and the $s$-wave scattering length.
The evolution of an interacting two-component Bose-Einstein condensate from an initial phase state leads to a spin squeezed state that may be used in atomic clocks to increase the signal-to-noise ratio, opening the way to quantum metrology. The efficiency of spin squeezing is limited by the finite temperature of the gas, as was shown theoretically in a spatially homogeneous system. Here we determine the limit of spin squeezing in the realistic trapped case, with classical field simulations, and with a completely analytical treatment that includes the quantum case.
We study the joint effects of vector and tensor light shifts in a set of large spin atoms, prepared in a polarized state and interacting with light. Depending on the ratio $ε$ between tensor and vector coupling and a measurement rate $Γ$, we identify a regime of quantum non-demolition measurement squeezing for times shorter than $(\sqrtεΓ)^{-1}$, and a deterministic squeezing regime for times longer than $(εΓ)^{-1}$. We apply our results to fermionic isotopes of strontium, ytterbium, and helium, which are atoms with purely nuclear spin in their ground state, benefiting from very low decoherence. For ytterbium 173, with a cavity such as that of \cite{Thompson2021}, it would be possible to achieve an atomic spin variance reduction of $0.03$ in $\simeq 50 \rm ms$.
In quantum metrology, entangled states of many-particle systems are investigated to enhance measurement precision of the most precise clocks and field sensors. While single-parameter quantum metrology is well established, many metrological tasks require joint multiparameter estimation, which poses new conceptual challenges that have so far only been explored theoretically. We experimentally demonstrate multiparameter quantum metrology with an array of entangled atomic ensembles. By splitting a spin-squeezed ensemble, we create an atomic sensor array featuring inter-sensor entanglement that can be flexibly configured to enhance measurement precision of multiple parameters jointly. Using an optimal estimation protocol, we achieve significant gains over the standard quantum limit in key multiparameter estimation tasks, thus grounding the concept of quantum enhancement of field sensor arrays and imaging devices.
Bell non-locality stems from quantum correlations effectively identified using inequalities. Spin chains, simulated with ultra-cold atoms in optical lattices, Rydberg atoms in tweezer arrays, trapped ions, or molecules, allow single-spin control and measurement. Therefore, they are suitable for studying fundamental aspects of these correlations and non-locality. Occupation defects, such as vacancies or multiple atoms occupying a single site due to imperfect system preparation, limit the detection of Bell correlations. We study their effects with the help of a simplified toy model parameterised by the probability $p$ of having a single occupation for a given site. Within this model, and for entangled systems obtained by one-axis twisting evolution from an initial factorised state, we derive two Bell inequalities, one based on many-site correlations and the other on two-site correlations, and identify the smallest probability $p$ that allows the Bell inequalities violation to be detected. We then consider two physical realizations using entangled ultra-cold atoms in optical lattices where the parameter $p$ is related to a non-unitary filling factor and non-zero temperature. We test the predictions of the toy model against exact numerical results.
We derive the semiclassical evolution equations for a system consisting of helium-3 atoms in the $2^3S$ metastable state interacting with a light field far-detuned from the $2^3S-2^3P$ transition, in the presence of metastability exchange collisions with ground state helium atoms and a static magnetic field. For two configurations, each corresponding to a particular choice of atom-light detuning in which the contribution of either the metastable level $F=1/2$ or $F=3/2$ is dominant, we derive a simple model of three coupled collective spins from which we can analytically extract an effective coupling constant between the collective nuclear spin and light. In these two configurations, we compare the predictions of our simplified model with the full model.
It is generally accepted that the phonon gas of a superfluid always enters a weak coupling regime at sufficiently low temperatures, whatever the strength of the interactions between the underlying particles (constitutive of the superfluid). Thus, in this limit, we should always be able to calculate the damping rate of thermal phonons by applying Fermi's golden rule to the Hamiltonian $H_3$ of cubic phonon-phonon coupling taken from quantum hydrodynamics, at least in the case of a convex acoustic branch and in the collisionless regime (where the eigenfrequency of the considered phonons remains much greater than the gas thermalization rate). Using the many-body Green's function method, we predict that, unexpectedly, this is not true in two dimensions, contrary to the three-dimensional case. We confirm this prediction with classical phonon-field simulations and a non-perturbative theory in $H_3$, where the fourth order is regularized by hand, giving a complex energy to the virtual phonons of the four-phonon collisional processes. For a weakly interacting fluid and a phonon mode in the long-wavelength limit, we predict a damping rate about three times lower than that of the golden rule.
Using the platform of a trapped-atom clock on a chip, we observe the time evolution of spin-squeezed hyperfine clock states in ultracold rubidium atoms on previously inaccessible timescales up to 1 s. The spin degree-of-freedom remains squeezed after 0.6 s, which is consistent with the limit imposed by particle loss and is compatible with typical Ramsey times in state-of-the-art microwave clocks. The results also reveal a surprising spin-exchange interaction effect that amplifies the cavity-based spin measurement via a correlation between spin and external degrees of freedom. These results open up perspectives for squeezing-enhanced atomic clocks in a metrologically relevant regime and highlight the importance of spin interactions in real-life applications of spin squeezing.
We show that a significant quantum gain corresponding to squeezed or over-squeezed spin states can be obtained in multiparameter estimation by measuring the Hadamard coefficients of a 1D or 2D signal. The physical platform we consider consists of twolevel atoms in an optical lattice in a squeezed-Mott configuration, or more generally by correlated spins distributed in spatially separated modes. Our protocol requires the possibility to locally flip the spins, but relies on collective measurements. We give examples of applications to scalar or vector field mapping and compressed sensing.
Spin-squeezing is a well-established "quantum technology", where well-designed correlations in an ensemble of two-level systems reduce the statistical uncertainty of spectroscopic experiments. This paper reviews some important advances in the field, with emphasis on the author's contributions concerning in particular the fundamental limits imposed by decoherence. Building on the material presented in the first part, new ideas and some promising developments are outlined in the last section.
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 to take advantage of the weak coupling of ground-state helium-3 nuclear spin to its environment to produce long-lived macroscopic quantum states, nuclear spin squeezed states, in a gas cell at room temperature. To perform a quantum non-demolition measurement of a transverse component of the polarized collective nuclear spin, we maintain a population in helium-3 metastable state with a discharge. The collective spin associated to $F=1/2$ metastable level hybridizes with the ground state one by metastability exchange collisions. To access nuclear spin fluctuations, one continuously measures the light leaking out of an optical cavity, where it has interacted dispersively with the metastable state collective spin. In a three coupled collective spin model (nuclear, metastable and Stokes), we calculate moments of the nuclear spin squeezed component $I_z$ conditioned on the time averaged optical signal. In the photon counting scheme, the squeezed observable is $I_z^2$ rather than $I_z$. In the homodyne detection scheme, we solve the stochastic equation for the system state conditioned on the measurement; the conditional expectation value of $I_z$ depends linearly on the signal and the conditional variance of $I_z$ does not depend on it. The conditional variance decreases as $(Γ_{\rm sq}t)^{-1}$, where the squeezing rate $Γ_{\rm sq}$ 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. Including de-excitation of metastable atoms at the walls, which induces nuclear spin decoherence with an effective rate $γ_α$, we find a limit $\propto(γ_α/Γ_{\rm sq})^{1/2}$ on the conditional variance reached in a time $\propto(γ_αΓ_{\rm sq})^{-1/2}$.
We propose a technique to control the macroscopic collective nuclear spin of a Helium-3 vapor in the quantum regime using light. The scheme relies on metastability exchange collisions to mediate interactions between optically accessible metastable states and the ground-state nuclear spin, giving rise to an effective nuclear spin-light quantum nondemolition interaction of the Faraday form. Our technique enables measurement-based quantum control of nuclear spins, such as the preparation of spin-squeezed states. This, combined with the day-long coherence time of nuclear spin states in Helium-3, opens the possibility for a number of applications in quantum technology.
Liquid helium and spin-1/2 cold-atom Fermi gases both exhibit in their superfluid phase two distinct types of excitations, gapless phonons and gapped rotons or fermionic pair-breaking excitations. In the long wavelength limit, revising and extending Landau and Khalatnikov's theory initially developed for helium [ZhETF 19, 637 (1949)], we obtain universal expressions for three- and four-body couplings among these two types of excitations. We calculate the corresponding phonon damping rates at low temperature and compare them to those of a pure phononic origin in high-pressure liquid helium and in strongly interacting Fermi gases, paving the way to experimental observations.
We study the condensate phase dynamics in a low-temperature equilibrium gas of weakly interacting bosons, harmonically trapped and isolated from the environment. We find that at long times, much longer than the collision time between Bogoliubov quasiparticles, the variance of the phase accumulated by the condensate grows with a ballistic term quadratic in time and a diffusive term affine in time. We give the corresponding analytical expressions in the limit of a large system, in the collisionless regime and in the ergodic approximation for the quasiparticle motion. When properly rescaled, they are described by universal functions of the temperature divided by the Thomas-Fermi chemical potential. The same conclusion holds for the mode damping rates. Such universality class differs from the previously studied one of the homogeneous gas.
We propose a method to obtain a regular arrangement of two-level atoms in a three-dimensional optical lattice with unit filling, where all the atoms share internal state coherence and metrologically useful quantum correlations. Such a spin-squeezed atomic crystal is obtained by adiabatically raising an optical lattice in an interacting two-component Bose-Einstein condensate. The scheme could be directly implemented on a microwave transition with state-of-the art techniques and used in optical-lattice atomic clocks with bosonic atoms to strongly suppress the collisional shift and benefit from the spins quantum correlations at the same time.
Using the time-dependent Bogoliubov approach, we study adiabaticity for a two-component Bose-Einstein condensate in a 3D time-dependent optical lattice with unit filling, in the superfluid and weakly interacting regime. We show that raising the lattice potential height can couple the ground state of the Bogoliubov Hamiltonian to excited states with two quasiparticles of opposite quasi-momenta. In the symmetric case for interactions and density in the two components these represent sound waves where the two components oscillate out of phase. We find an analytic expression of the adiabatic time, its dependence on the fraction of atoms in each component and its scaling with the system size.