Entanglement, a key feature of quantum mechanics, is a resource that allows the improvement of precision measurements beyond the conventional bound reachable by classical means. This is known as the standard quantum limit, already defining the accuracy of the best available sensors for various quantities such as time or position. Many of these sensors are interferometers in which the standard quantum limit can be overcome by feeding their two input ports with quantum-entangled states, in particular spin squeezed states. For atomic interferometers, Bose-Einstein condensates of ultracold atoms are considered good candidates to provide such states involving a large number of particles. In this letter, we demonstrate their experimental realization by splitting a condensate in a few parts using a lattice potential. Site resolved detection of the atoms allows the measurement of the conjugated variables atom number difference and relative phase. The observed fluctuations imply entanglement between the particles, a resource that would allow a precision gain of 3.8 dB over the standard quantum limit for interferometric measurements.
Efficient control of spin squeezing in a two-component Bose-Einstein Condensate is studied by rapidly turning-off the external field at a time that maximal spin squeezing appears. We show that strong reduction of spin fluctuation can be maintained in a nearly fixed direction for a long time. We explain the underlying physics unambiguously, and present analytical expressions of the maximal-squeezing time.
We investigate spin squeezing of a two-mode boson system with a Josephson coupling. An exact relation between the squeezing and the single-particle coherence at the maximal-squeezing time is discovered, which provides a more direct way to measure the squeezing by readout the coherence in atomic interference experiments. We prove explicitly that the strongest squeezing is along the $J_z$ axis, indicating the appearance of atom number-squeezed state. Power laws of the strongest squeezing and the optimal coupling with particle number $N$ are obtained based upon a wide range of numerical simulatio…
We study atom-atom correlations and relative number squeezing in the dissociation of a Bose-Einstein condensate (BEC) of molecular dimers made of either bosonic or fermionic atom pairs. Our treatment addresses the role of the spatial inhomogeneity of the molecular BEC on the strength of correlations in the short time limit. We obtain explicit analytic results for the density-density correlation functions in momentum space, and show that the correlation widths and the degree of relative number squeezing are determined merely by the shape of the molecular condensate.
We optimize number squeezing when splitting a mesoscopic Bose Einstein condensate. Applying optimal control theory to a realistic description of the condensate allowed us to identify a form of the splitting ramp which drastically outperforms the adiabatic splitting. The results can be interpreted in terms of a generic two-mode model mapped onto a parametric harmonic oscillator. This optimal route to squeezing paves the way to a much longer phase coherence and atom interferometry close to the Heisenberg limit.
We develop a scheme to generate number squeezing in a Bose-Einstein condensate by utilizing interference between two hyperfine levels and nonlinear atomic interactions. We describe the scheme using a multimode quantum field model and find agreement with a simple analytic model in certain regimes. We demonstrate that the scheme gives strong squeezing for realistic choices of parameters and atomic species. The number squeezing can result in noise well below the quantum limit, even if the initial noise on the system is classical and much greater than that of a poisson distribution.
We examine the properties of an atom laser produced by outcoupling from a Bose-Einstein condensate with squeezed light. We model the multimode dynamics of the output field and show that a significant amount of squeezing can be transfered from an optical mode to a propagating atom laser beam. We use this to demonstrate that two-mode squeezing can be used to produce twin atom laser beams with continuous variable entanglement in amplitude and phase.
We measured the relative phase of two Bose-Einstein condensates confined in an radio frequency induced double well potential on an atom chip. We observed phase coherence between the separated condensates for times up to 200 ms after splitting, a factor of 10 beyond the phase diffusion limit expected for a coherent state in our experimental conditions (20 ms). The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrated a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split conden…
Dynamical evolution of quantum mechanical squeezing and entanglement in a two-mode Bose-Einstein condensate (TBEC) with an adiabatic, time-varying Raman coupling is studied by finding analytical expressions for these quantities. In particular, we study the entanglement between the atoms in the condensate as well as that between the two modes. The nature of the enhanced quantum correlations in TBEC is clarified by considering squeezing and entanglement both with and without the nonlinear interaction turned on; it is found that entanglement approaching maximal value can be achieved with the nonl…
We investigate the presence of squeezing in the weakly repulsive uniform Bose gas, in both the condensate mode and in the nonzero opposite-momenta mode pairs, using two different variational formulations. We explore the U(1) symmetry breaking and Goldstone's theorem in the context of a squeezed coherent variational wavefunction, and present the associated Ward identity. We show that squeezing of the condensate mode is absent at the mean field Hartree-Fock-Bogoliubov level and emerges as a result of fluctuations about mean field as a finite volume effect, which vanishes in the thermodynamic lim…
We theoretically analyze atom interferometry based on trapped ultracold atoms, and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) c…
We analyze the dynamics of quantum statistics in a harmonically trapped Bose-Einstein condensate, whose two-body interaction strength is controlled via a Feshbach resonance. From an initially non-interacting coherent state, the quantum field undergoes Kerr squeezing, which can be qualitatively described with a single mode model. To render the effect experimentally accessible, we propose a homodyne scheme, based on two hyperfine components, which converts the quadrature squeezing into number squeezing. The scheme is numerically demonstrated using a two-component Hartree-Fock-Bogoliubov formalis…
We derive and analyze shock-wave solutions of hydrodynamic equations describing repulsively interacting one dimensional Bose gas. We also use the number-conserving Bogolubov approach to verify accuracy of the Gross-Pitaevskii equation in shock wave problems. We show that quantum corrections to dynamics of shocks (dark-shock-originated solitons) in a Bose-Einstein condensate are negligible (important) for a realistic set of system parameters. We point out possible signatures of a Bose-Einstein condensate -- Tonks crossover in shock dynamics. Our findings can be directly verified in different ex…
Light with a chemical potential and no mass is shown to possess a general phase-transition curve to Bose-Einstein condensation. This limiting density and temperature range is found by the diverging in-medium potential range of effective interaction. The inverse expansion series of the effective interaction from Bethe-Salpeter equation is employed exceeding the ladder approximation. While usually the absorption and emission with Dye molecules is considered, here it is proposed that squeezing can create also such a mean interaction leading to a chemical potential. The equivalence of squeezed lig…
We present a statistical description of Bose-Einstein condensates with general higher order nonlinearities. In particular, we investigate the case of cubic-quintic nonlinearities, of particular interest for dilute condensates. The implication of decoherence for the stability properties of the condensate is discussed.
We study an ultracold Bose gas in the presence of 1D disorder for repulsive inter-atomic interactions varying from zero to the Thomas-Fermi regime. We show that for weak interactions the Bose gas populates a finite number of localized single-particle Lifshits states, while for strong interactions a delocalized disordered Bose-Einstein condensate is formed. We discuss the schematic quantum-state diagram and derive the equations of state for various regimes.
We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensate, the popular Gross-Pitaevskii theory and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensate, with the U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like…
We compare the collective modes for Bose-condensed systems with two degenerate components with and without spontaneous intercomponent coherence at finite temperature using the time-dependent Hartree-Fock approximation. We show that the interaction between the condensate and non-condensate in these two cases results in qualitatively different collective excitation spectra. We show that at zero temperature the single-particle excitations of the incoherent Bose condensate can be probed by intercomponent excitations.
We study the temperature dependence of single-particle and pair coherent condensate densities for a Bose liquid with a "depleted" single-particle Bose-Einstein condensate (BEC) at $T \neq 0$. Our investigations were based on the field-theoretical Green's functions. On the basis of the use of empirical data about the speeds of the first and second sounds is described superfluid state at $T \neq 0$. It is studied the structure of superfluid state taking into account appearance with the different from zero temperatures of normal component and taking into account the branch of the second sound, wh…
We observe the formation of momentum distributions indicative of spatial period-doubling of superfluid Bose-Einstein condensates in periodically translated optical lattices. The effect is attributed to dynamic instability of the condensate wavefunction caused by modulation-induced coupling of ground and excited bands.
We show that it is possible to observe matter wave interference patterns in the collision of bright solitons (Bose Einstein condensates) without free ballistic expansion for suitable choices of scattering length and time dependent trap.
I discuss a Bogoliubov inequality for obtaining a rigorous bound on the maximal axial extension of inhomogeneous one-dimensional Bose-Einstein condensates. An explicit upper limit for the aspect ratio of a strongly elongated, harmonically trapped Thomas-Fermi condensate is derived.
How does a rapidly rotating condensed Bose gas carry extreme amounts of angular momentum? The energetically favored state of a not-too-rapidly rotating Bose condensed gas is, as observed, a triangular lattice of singly quantized vortices. This paper describes the fates of the vortex lattice in both harmonic and anharmonic traps when condensates are rotated extremely rapidly.
The general properties of the order parameter for a dipolar spinor Bose-Einstein condensate are discussed based on symmetries of interactions. An initially spin-polarized dipolar condensate is shown to dynamically generate a non-singular vortex via spin-orbit interactions -- a phenomenon reminiscent of the Einstein--de Haas effect in ferromagnets.
We investigate the dynamics of doubly charged vortices generated in dilute Bose-Einstein condensates by using the topological phase imprinting technique. We find splitting times of such vortices and show that thermal atoms are responsible for their decay.
Under a unified theory we investigate the formation of various types of vector-solitons in two-species Bose-Einstein condensates with arbitrary scattering lengths. We then show that by tuning the interaction parameter via Feshbach resonance, transformation between different types of vector solitons is possible. Our results open up new ways in the quantum control of multi-species Bose-Einstein condensates.
We argue that the main mechanism for condensate collapse in an attractive Bose-Einstein condensate is the loss of coherence between atoms a finite distance apart, rather than the growth of the occupation number in noncondensate modes. Since the former mechanism is faster than the latter by a factor of approximately 3/2, this helps to dispel the apparent failure of field theoretical models in predicting the collapse time of the condensate.
We derive the dynamic and thermodynamic stability conditions for dilute multicomponent Bose-Einstein condensates (BECs). These stability conditions, generalized for $n$-component BECs, are found to be equivalent and are shown to be consistent with the phase diagrams of two- and three-component condensates that are derived from energetic arguments.
In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic con…
We show that knots of spin textures can be created in the polar phase of a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation and probe, together with their lifetime.
