arXiv subjects

Alice Sinatra

Publications and source records attributed to Alice Sinatra.

At least 37 records · Page 2Linked to original sources

arXiv2018

Spontanous spin squezing in a rubidium BEC

We describe an experiment where spin squeezing occurs spontaneously within a standard Ramsey sequence driving a two-component Bose-Einstein condensate (BEC) of 87Rb atoms trapped in an elongated magnetic trap. Multiparticle entanglement 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+/-0.4dB 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.

cond-mat.quant-gas↗

arXiv2017

Three-phonon and four-phonon interaction processes in a pair-condensed Fermi gas

We study the interactions among phonons and the phonon lifetime in a pair-condensed Fermi gas in the BEC-BCS crossover in the collisionless regime. To compute the phonon-phonon coupling amplitudes we use a microscopic model based on a generalized BCS Ansatz including moving pairs, which allows for a systematic expansion around the mean field BCS approximation of the ground state. We show that the quantum hydrodynamic expression of the amplitudes obtained by Landau and Khalatnikov apply only on the energy shell, that is for resonant processes that conserve energy. The microscopic model yields the same excitation spectrum as the Random Phase Approximation, with a linear (phononic) start and a concavity at low wave number that changes from upwards to downwards in the BEC-BCS crossover. When the concavity of the dispersion relation is upwards at low wave number, the leading damping mechanism at low temperature is the Beliaev-Landau process 2 phonons $\leftrightarrow$ 1 phonon while, when the concavity is downwards, it is the Landau-Khalatnikov process 2 phonons $\leftrightarrow$ 2 phonons. In both cases, by rescaling the wave vectors to absorb the dependence on the interaction strength, we obtain a universal formula for the damping rate. This universal formula corrects and extends the original analytic results of Landau and Khalatnikov [ZhETF {\bf 19}, 637 (1949)] for the $2\leftrightarrow2$ processes in the downward concavity case. In the upward concavity case, for the Beliaev 1$\leftrightarrow$ 2 process for the unitary gas at zero temperature, we calculate the damping rate of an excitation with wave number $q$ including the first correction proportional to $q^7$ to the $q^5$ hydrodynamic prediction, which was never done before in a systematic way.

cond-mat.quant-gas↗

arXiv2017

EPR-entangled Bose-Einstein condensates in state-dependent potentials: a dynamical study

We study generation of non-local correlations by atomic interactions in a pair of bi-modal Bose-Einstein Condensates in state-dependent potentials including spatial dynamics. The wave-functions of the four components are described by combining a Fock state expansion with a time-dependent Hartree-Fock Ansatz, so that both the spatial dynamics and the local and non-local quantum correlations are accounted for. We find that despite the spatial dynamics, our protocole generates enough non-local entanglement to perform an EPR steering experiment with two spatially separated con-densates of a few thousands of atoms.

quant-ph↗

arXiv2017

Mesoscopic quantum superpositions in bimodal Bose-Einstein condensates: decoherence and strategies to counteract it

We study theoretically the interaction-induced generation of mesoscopic coherent spin state superpositions (small cat states) from an initial coherent spin state in bimodal Bose-Einstein condensates and the subsequent phase revival, including decoherence due to particle losses and fluctuations of the total particle number. In a full multimode description, we propose a preparation procedure of the initial coherent spin state and we study the effect of preexisting thermal fluctuations on the phase revival, and on the spin and orbito-spinorial cat fidelities.

cond-mat.quant-gas↗

arXiv2017

Landau-Khalatnikov phonon damping in strongly interacting Fermi gases

We derive the phonon damping rate due to the four-phonon Landau-Khalatnikov process in low temperature strongly interacting Fermi gases using quantum hydrodynamics, correcting and extending the original calculation of Landau and Khalatnikov [ZhETF, 19 (1949) 637]. Our predictions can be tested in state-of-the-art experiments with cold atomic gases in the collisionless regime.

cond-mat.quant-gas↗

arXiv2016

Thermal blurring of a coherent Fermi gas

It is generally assumed that a condensate of paired fermions at equilibrium is characterized by a macroscopic wavefunction with a well-defined, immutable phase. In reality, all systems have a finite size and are prepared at non-zero temperature; the condensate has then a finite coherence time, even when the system is isolated in its evolution and the particle number $N$ is fixed. The loss of phase memory is due to interactions of the condensate with the excited modes that constitute a dephasing environment. This fundamental effect, crucial for applications using the condensate of pairs' macroscopic coherence, was scarcely studied. We link the coherence time to the condensate phase dynamics, and we show with a microscopic theory that the time derivative of the condensate phase operator $\hatθ\_0$ is proportional to a chemical potential operator that we construct including both the pair-breaking and pair-motion excitation branches. In a single realization of energy $E$, $\hatθ\_0$ evolves at long times as $-2μ\_{\rm mc}(E)t/\hbar$ where $μ\_{\rm mc}(E)$ is the microcanonical chemical potential; energy fluctuations from one realization to the other then lead to a ballistic spreading of the phase and to a Gaussian decay of the temporal coherence function with a characteristic time $\propto N^{1/2}$. In the absence of energy fluctuations, the coherence time scales as $N$ due to the diffusive motion of $\hatθ\_0$. We propose a method to measure the coherence time with ultracold atoms, which we predict to be tens of milliseconds for the canonical ensemble unitary Fermi gas.

cond-mat.quant-gas↗

arXiv2015

Limits of atomic entanglement by cavity-feedback : from weak to strong coupling

We theoretically investigate the entangled states of an atomic ensemble that can be obtained via cavity-feedback, varying the atom-light coupling from weak to strong, and including a systematic treatment of decoherence. In the strong coupling regime for small atomic ensembles, the system is driven by cavity losses into a long-lived, highly-entangled many-body state that we characterize analytically. In the weak coupling regime for large ensembles, we find analytically the maximum spin squeezing that can be achieved by optimizing both the coupling and the atom number. This squeezing is fundamentally limited by spontaneous emission to a constant value, independent of the atom number. Harnessing entanglement in many-body systems is of fundamental interest [1] and is the key requirement for quantum enhanced technologies, in particular quantum metrology [2]. In this respect, many efforts have been devoted to prepare entangled states in atomic ensembles because of their high degree of coherence and their potential for precision measurement. Spin squeezed states as well as number states have been produced following methods based either on coherent evolution in the presence of a non-linearity in the atomic field [3--5], or on quantum non-demolition measurement [6--8]. Among methods of the first kind, cavity feedback [5, 9] is one of the most promising: it has already allowed for the creation of highly squeezed states [5] and the effective non-linearity introduced by the atom-cavity coupling can be easily switched off, making it very attractive for metrol-ogy applications. In this Letter, we analyze the entangled states that can be produced by cavity feedback in different coupling regimes from weak to strong, and derive the ultimate limits of the metrology gain, extending the optimization of squeezing to unexplored domains of parameters values. After optimization of both the coupling strength and the atom number, we find a maximum squeezing limit that depends only on the atomic structure.

quant-ph↗

arXiv2013

Phase operators and blurring time of a pair-condensed Fermi gas

Due to atomic interactions and dispersion in the total atom number, the order parameter of a pair-condensed Fermi gas experiences a collapse in a time that we derive microscopically. As in the bosonic case, this blurring time depends on the derivative of the gas chemical potential with respect to the atom number and on the variance of that atom number. The result is obtained first using linearized time-dependent Bogoliubov-de Gennes equations, then in the Random Phase Approximation, and then it is generalized to beyond mean field. In this framework, we construct and compare two phase operators for the paired fermionic field: The first one, issued from our study of the dynamics, is the infinitesimal generator of adiabatic translations in the total number of pairs. The second one is the phase operator of the amplitude of the field of pairs on the condensate mode. We explain that these two operators differ due to the dependence of the condensate wave function on the atom number.

cond-mat.quant-gas↗

arXiv2013

Spin squeezing and EPR entanglement of two bimodal condensates in state-dependent potentials

We propose and analyze a scheme to entangle the collective spin states of two spatially separated bimodal Bose-Einstein condensates. Using a four-mode approximation for the atomic field, we show that elastic collisions in a state-dependent potential simultaneously create spin-squeezing in each condensate and entangle the collective spins of the two condensates. We investigate mostly analytically the non-local quantum correlations that arise in this system at short times and show that Einstein-Podolsky-Rosen (EPR) entanglement is generated between the condensates. At long times we point out macroscopic entangled states and explain their structure. The scheme can be implemented with condensates in state-dependent microwave potentials on an atom chip.

cond-mat.quant-gas↗

arXiv2012

Spin Squeezing in Finite Temperature Bose-Einstein Condensates : Scaling with the system size

We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number $N\to \infty$ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: 1/N in the thermodynamic limit and the non-condensed fraction $ /N$ in the Bogoliubov limit. To test our analytical results beyond the Bogoliubov approximation, and to perform numerical experiments, we use improved classical field simulations with a carefully chosen cut-off, such that the classical field model gives for the ideal Bose gas the correct non-condensed fraction in the Bose-condensed regime.

quant-ph↗

arXiv2012

Spatial and temporal coherence of a Bose-condensed gas

The central problem of this chapter is temporal coherence of a three-dimensional spatially homogeneous Bose-condensed gas, initially prepared at finite temperature and then evolving as an isolated interacting system. A first theoretical tool is a number-conserving Bogoliubov approach that allows to describe the system as a weakly interacting gas of quasi-particles. This approach naturally introduces the phase operator of the condensate: a central actor since loss of temporal coherence is governed by the spreading of the condensate phase-change. A second tool is the set of kinetic equations describing the Beliaev-Landau processes for the quasi-particles. We find that in general the variance of the condensate phase-change at long times $t$ is the sum of a ballistic term $\propto t^2$ and a diffusive term $\propto t$ with temperature and interaction dependent coefficients. In the thermodynamic limit, the diffusion coefficient scales as the inverse of the system volume. The coefficient of $t^2$ scales as the inverse volume squared times the variance of the energy of the system in the initial state and can also be obtained by a quantum ergodic theory (the so-called eigenstate thermalisation hypothesis).

cond-mat.quant-gas↗

arXiv2011

Spin squeezing in Bose-Einstein condensates: Limits imposed by decoherence and non-zero temperature

We consider dynamically generated spin squeezing in interacting bimodal condensates. We show that particle losses and non-zero temperature effects in a multimode theory completely change the scaling of the best squeezing for large atom numbers. We present the new scalings and we give approximate analytical expressions for the squeezing in the thermodynamic limit. Besides reviewing our recent theoretical results, we give here a simple physical picture of how decoherence acts to limit the squeezing. We show in particular that under certain conditions the decoherence due to losses and non-zero temperatureacts as a simple dephasing.

cond-mat.quant-gas↗

arXiv2010

Enhanced and reduced atom number fluctuations in a BEC splitter

We measure atom number statistics after splitting a gas of ultracold 87Rb atoms in a purely magnetic double-well potential created on an atom chip. Well below the critical temperature for Bose-Einstein condensation T_c, we observe reduced fluctuations down to -4.9dB below the atom shot noise level. Fluctuations rise to more than +3.8dB close to T_c, before reaching the shot noise level for higher temperatures. We use two-mode and classical field simulations to model these results. This allows us to confirm that the super-shot noise fluctuations directly originate from quantum statistics.

quant-ph↗

arXiv2010

Atom chip based generation of entanglement for quantum metrology

Atom chips provide a versatile `quantum laboratory on a microchip' for experiments with ultracold atomic gases. They have been used in experiments on diverse topics such as low-dimensional quantum gases, cavity quantum electrodynamics, atom-surface interactions, and chip-based atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations, quantum information processing, and quantum metrology. Here we report experiments where we generate multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential. We employ this technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are useful for quantum metrology. The observed 3.7 dB reduction in spin noise combined with the spin coherence imply four-partite entanglement between the condensate atoms and could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. Our data show good agreement with a dynamical multi-mode simulation and allow us to reconstruct the Wigner function of the spin-squeezed condensate. The techniques demonstrated here could be directly applied in chip-based atomic clocks which are currently being set up.

quant-ph↗

arXiv2010

Particle number fluctuations in a cloven trapped Bose gas at finite temperature

We study fluctuations in the atom number difference between two halves of a harmonically trapped Bose gas in three dimensions. We solve the problem analytically for non interacting atoms. In the interacting case we find an analytical solution in the Thomas-Fermi and high temperature limit in good agreement with classical field simulations. In the large system size limit, fluctuations in the number difference are maximal for a temperature $T\simeq 0.7 T_c$ where $T_c$ is the critical temperature, independently of the trap anisotropy. The occurrence of this maximum is due to an interference effect between the condensate and the non-condensed field.

cond-mat.quant-gas↗

arXiv2009

Coherence time of a Bose-Einstein condensate

Temporal coherence is a fundamental property of macroscopic quantum systems, such as lasers in optics and Bose-Einstein condensates in atomic gases and it is a crucial issue for interferometry applications with light or matter waves. Whereas the laser is an "open" quantum system, ultracold atomic gases are weakly coupled to the environment and may be considered as isolated. The coherence time of a condensate is then intrinsic to the system and its derivation is out of the frame of laser theory. Using quantum kinetic theory, we predict that the interaction with non-condensed modes gradually smears out the condensate phase, with a variance growing as A t^2+B t+C at long times t, and we give a quantitative prediction for A, B and C. Whereas the coefficient A vanishes for vanishing energy fluctuations in the initial state, the coefficients B and C are remarkably insensitive to these fluctuations. The coefficient B describes a diffusive motion of the condensate phase that sets the ultimate limit to the condensate coherence time. We briefly discuss the possibility to observe the predicted phase spreading, also including the effect of particle losses.

cond-mat.quant-gas↗

arXiv2009

The truncated Wigner method for Bose condensed gases: limits of validity and applications

We study the truncated Wigner method (TWM) applied to a weakly interacting Bose condensed gas perturbed away from thermal equilibrium. The idea of the method is to generate an ensemble of classical fields which samples the Wigner function of the initial thermal density operator, and to evolve each field with the Gross-Pitaevskii equation (GPE). In the first part of the paper we improve the sampling technique over our previous work and we test its accuracy against the exactly solvable model of the ideal gas. In the second part of the paper we investigate the conditions of validity of the TWM. For short evolution times the time-dependent Bogoliubov approximation is valid for almost pure condensates. The requirement that the TWM reproduces the Bogoliubov prediction leads to the constraint that the number of field modes must be smaller than the number of particles.For longer times the nonlinear dynamics of the noncondensed modes plays an important role. To demonstrate this we analyse the case of a 3D spatially homogeneous Bose condensed gas and we test how well TWM reproduces Beliaev-Landau damping.We have identified the mechanism which limits the validity of the TWM: the initial classical fields, driven by the time-dependent GPE, thermalise to a classical field distribution at a temperature T_class larger than the initial temperature T. When T_class significantly exceeds T a spurious damping is observed in the simulation. This leads to the second condition for the TWM, T_class-T<<T, which requires that the maximum energy of the Bogoliubov modes does not exceed a few k_B T.

cond-mat.stat-mech↗

arXiv2008

Spin squeezing in a bimodal condensate: spatial dynamics and particle losses

We propose an analytical method to study the entangled spatial and spin dynamics of interacting bimodal Bose-Einstein condensates. We show that at particular times during the evolution spatial and spin dynamics disentangle and the spin squeezing can be predicted by a simple two-mode model. We calculate the maximum spin squeezing achievable in experimentally relevant situations with Sodium or Rubidium bimodal condensates, including the effect of the dynamics and of one, two and three-body losses.

quant-ph↗