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arXiv:1705.10643 · Physical Review A

Probing quantum states with momentum boosts

Tarek A. Elsayed, Alexej I. Streltsov

Published Jul 17, 2018• 7 citations
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Abstract

We present a technique to diagnose the condensate fraction in a one-dimensional optical lattice of weakly interacting bosons based on the dynamics of the trapped atoms under the influence of a momentum kick. It is shown using the multi-configuration time-dependent Hartree method for bosons that the two extreme cases of the superfluid and Mott insulator states exhibit different behaviors when the lattice is briefly tilted. The current induced by the momentum boost caused by the tilt which depends directly on the amount of phase coherence between the lattice sites is linearly proportional to the condensate fraction. The atom-atom interactions only change the slope of the linear relationship. We discuss the applications of this scheme in magnetic field gradiometery.

DOI
10.1103/physreva.98.013618

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We present a technique to diagnose the condensate fraction in a one-dimensional optical lattice of weakly interacting bosons based on the dynamics of the trapped atoms under the influence of a momentum kick. It is shown using the multi-configuration time-dependent Hartree method for bosons that the two extreme cases of the superfluid and Mott insulator states exhibit different behaviors when the lattice is briefly tilted. The current induced by the momentum boost caused by the tilt which depends directly on the amount of phase coherence between the lattice sites is linearly proportional to the condensate fraction. The atom-atom interactions only change the slope of the linear relationship. We discuss the applications of this scheme in magnetic field gradiometery.
We present a novel technique to diagnose the condensate fraction in an optical lattice of weakly-interacting bosons based on the dynamics of the trapped atoms under the influence of a momentum kick. It is shown using the Multi-Configuration Time Dependent Hartree method for Bosons (MCTDHB) that the two extreme cases of the superfluid and Mott insulator states exhibit different behaviors when the lattice is briefly tilted. The current induced by the momentum boost caused by the tilt depends directly on the amount of phase coherence between the lattice sites which in turn depends on the condensate fraction. The potential of using the relation between the frequency of the induced current and the amount of momentum boost imparted to the system in magnetic field gradiometery is also discussed.
We propose a method to probe states in the Mott insulator regime produced from a condensate in an optical lattice. We consider a system in which we create time-dependent number fluctuations in a given site by turning off the atomic interactions and lowering the potential barriers on a nearly pure Mott state to allow the atoms to tunnel between sites. We calculate the expected interference pattern and number fluctuations from such a system and show that one can potentially observe a deviation from a pure Mott state. We also discuss a method in which to detect these number fluctuations using time-of-flight imaging.
Quantum tunneling is one of the most fundamental processes in nature. Single particle hopping of ultracold atoms in optical lattices changes its character dramatically when the ensemble is prepared in strongly correlated quantum phases due to atom-atom interactions. Correlated hopping in a Mott-insulating chain of bosons that is tilted to the Mott gap has recently been employed to study long-range order in the 1D transvers Ising model [1,2]. We study correlated tunneling dynamics for an ensemble of tilted 1D Mott chains after a sudden quench to the vicinity of the Ising paramagnetic to antiferromagnetic phase transition point [3]. The quench results in coherent oscillations for the orientation of effective Ising spins, detected via oscillations in the number of doubly occupied lattice sites. We characterize the quench by varying the system parameters. We report significant modification of the tunneling rate induced by interactions and show clear evidence for collective effects in the oscillatory response. We observe higher-order many-body tunneling processes over up to five lattice sites when the tilt per site is tuned to integer fractions of the Mott gap. Secondand third-order tunneling shows up in the transient response after the quench, from which we extract the characteristic scaling in accordance with perturbation theory and numerical simulations. In a second set of experiments we study the response of an ensemble of 1D superfluids in the Bose-Hubbard regime when subject to a tilt [4]. For large values of the tilt, we observe interaction-induced coherent decay and matter-wave quantum phase revivals of the Bloch oscillating ensemble. We analyze the revival period dependence on interactions by means of a Feshbach resonance. When reducing the value of the tilt, we observe the disappearance of the quasi-periodic phase revival signature towards an irreversible decay of Bloch oscillations, indicating the transition from regular to quantum chaotic dynamics.
We discuss a technique to probe the properties of an interacting cold atomic gas that can be viewed as a dynamical compressibility measurement. We apply this technique to the study of the superfluid-to-Mott-insulator quantum phase transition in one and three dimensions for a bosonic gas trapped in an optical lattice. Excitations of the system are detected by time-of-flight measurements. The experimental data for the one-dimensional case are in good agreement with the results of a time-dependent density-matrix-renormalization-group calculation.
We experimentally probe the properties of the disordered Bose-Hubbard model using an atomic Bose-Einstein condensate trapped in a 3D disordered optical lattice. Controllable disorder is introduced using a fine-grained optical speckle field with features comparable in size to the lattice spacing along every lattice direction. A precision measurement of the disordering potential is used to compute the single-particle parameters of the system. To constrain theories of the disordered Bose Hubbard model, we have measured the change in condensate fraction as a function of disorder strength for several different ratios of tunneling to interaction energy. We observe disorder-induced, reversible suppression of condensate fraction for superfluid and coexisting superfluid-Mott-insulator phases.
Interacting bosons with two ``spin'' states in a lattice show superfluid-insulator phase transitions in the presence of spin-orbit coupling. Depending on the parameter regime, bosons in the superfluid phase can condense to either a zero-momentum state or to one or multiple states with finite momentum, leading to an unconventional superfluid phase. We study the response of such a system to modulation of the optical lattice potential. We show that the change in momentum distribution after lattice modulation shows distinct patterns in the Mott and the superfluid phase and these patterns can be used to detect these phases and the quantum phase transition between them. Further, the momentum-resolved optical modulation spectroscopy can identify both the gapless (Goldstone) and gapped amplitude (Higgs) mode of the superfluid phase and clearly distinguish between the superfluid phases with a zero-momentum condensate and a twisted superfluid phase by looking at the location of these modes in the Brillouin zone. We discuss experiments which can test our theory.