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arXiv:quant-ph/0609202 · Journal of the Optical Society of America B

Time reversal in an optical lattice

Fernando Cucchietti

Published Mar 9, 2010• 22 citations
arXivHTMLPDF

Abstract

Time reversal is an oft-used technique to probe and measure a quantum system. In particular, it is key for some theoretical information approaches to quantum criticality like fidelity decay. Here proposed is how to reverse the dynamics of cold bosonic atoms in an optical lattice in the regime described by the Bose-Hubbard model. The proposed experiment uses proven techniques—a linear phase imprint on the lattice, and a change in magnetic field to tune the boson-boson scattering length through a Feshbach resonance. The sensitivity of quantum dynamics across the insulator-superfluid quantum phase transition of the Bose-Hubbard model is studied, and sensing applications of dynamic reversals such as measuring the intensity of external potentials (e.g., gravity) is discussed.

DOI
10.1364/josab.27.000a30

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The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.

arXiv:cond-mat/9805329•Physical Review Letters•Oct 12, 1998•3,677 citations
Time reversal is an oft-used technique to probe and measure a quantum system. In particular, it is key for some theoretical information approaches to quantum criticality like fidelity decay. Here proposed is how to reverse the dynamics of cold bosonic atoms in an optical lattice in the regime described by the Bose-Hubbard model. The proposed experiment uses proven techniques—a linear phase imprint on the lattice, and a change in magnetic field to tune the boson-boson scattering length through a Feshbach resonance. The sensitivity of quantum dynamics across the insulator-superfluid quantum phase transition of the Bose-Hubbard model is studied, and sensing applications of dynamic reversals such as measuring the intensity of external potentials (e.g., gravity) is discussed.
Cold atoms in optical lattices provide a unique medium for mimicking effects known from other areas of physics. This is primarily due to a great flexibility and a precise manipulation of the cold atomic system [1–3]. Atoms of a fermionic or bosonic character may be placed in an optical lattice potential whose geometry may be easily controlled by changing polarizations of laser beams. Interactions between atoms may be controlled via magnetic, optical or microwave Feshbach resonances [4, 5] as well as via changing the depth of the optical lattice. The latter modifies primarily the tunneling between lattice sites, enabling e.g. the superfluid-Mott insulator quantum phase transition in the optical realization of the Bose-Hubbard model as proposed by Jaksch and Zoller [6] and subse
An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the interest in these systems is that the effects of the interatomic interactions can be strongly enhanced. More specifically, it has been shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-Einstein condensate into an optical lattice it is possible for the system to undergo a quantum phase transition to a new quantum phase of matter, the so-called Mott insulator phase. Within this Mott insulator phase each lattice site is occupied by exactly one atom. This makes the Mott insulator phase especially well suited for applications in the field of quantum computation and quantum information processing. We have theoretically investigated the above mentioned quantum phase transition and our formalism allows for a description of the Mott insulator phase at nonzero temperatures. Another important experimental development in the field of ultracold atomic gases is the use of Feshbach resonances to control the interatomic interactions. Such a resonance occurs whenever two colliding atoms form a long-lived molecule for some time. The crucial point of a Feshbach resonance is that the above mentioned molecule has a magnetic moment that is not equal to twice the magnetic moment of the atom. As a consequence the energy difference between the two atoms and the molecule and hence the interactions between the atoms can be controlled by using an external magnetic field. By combining these two techniques, i.e, by trapping ultracold atomic gases in an optical lattice and by tuning a magnetic field near a Feshbach resonance there can be a new quantum phase transition between two superfluid phases. We gave derived the the theory for the description of these Feshbach resonances in optical lattices and applied it to various systems. To be a bit more precise, if we tune the external magnetic field such that the energy difference between a molecule and two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate of molecules. In contrast, if the energy difference is large enough and positive we have a gas that consists primarily of a Bose-Einstein condensate of atoms. It turns out that these two limits are separated by an Ising-like quantum phase transition. By using atomic Bose gases near a Feshbach resonance detailed experimental studies which test the theoretical predictions of the statistical and dynamical properties of these quantum phase transitions can be made.
Manipulation of ultracold atoms in optical lattices is one of the optimal ways to observe phase transitions of the Hubbard model which is useful in a variety of condensed-matter systems. Bosonic atoms in this model experience a phase transition from superfluids to Mott insulators by tuning systematic parameters. However, in conventional setups, phase transitions take place over a large range of parameters instead of one critical point due to the background inhomogeneity caused by the Gaussian shape of optical-lattice lasers. To probe the phase transition point more precisely in our lattice system, we apply a blue-detuned laser to compensate for this local Gaussian geometry. By inspecting the change of visibility, we find a sudden jump point at one particular trap depth of optical lattices, corresponding to the first appearance of Mott insulators in inhomogeneous systems. This provides a simple method to detect the phase transition point in such inhomogeneous systems. We believe it will be a useful tool for most cold atom experiments.
The quantum phase transition from the Mott insulator to the superfluid phases of the bosonic atoms trapped in an optical lattice, in which the on-site interaction can be tuned by a Feshbach resonance, is investigated by a variational approach within mean-field theory. We derive an extended Bose-Hubbard model to describe this ultracold atomic system. By theoretical calculation and analysis, the phase diagram is shown clearly, and we find an exciting and novel phenomenon that is the appearance of the Mott insulator-sea (MI-sea). Meanwhile, the experimental feasibility of observing the MI-sea is discussed by analyzing the published data related to the Fashbach resonance at present. Finally, the potential application of the MI-sea for quantum information processing and quantum computation is also discussed in detail.
The Bose-Hubbard model is the simplest model of interacting bosons on a lattice. It has recently been the focus of much attention due to the realization of this model with cold atoms in an optical lattice. The ability to tune parameters in the Hamiltonian as a function of time in cold atom systems has opened up the possibility of studying out-of-equilibrium dynamics, including crossing the quantum critical region of the model in a controlled way. In this paper, I give a brief introduction to the Bose Hubbard model, and its experimental realization and then give an account of theoretical and experimental efforts to understand out-of-equilibrium dynamics in this model, focusing on quantum quenches, both instantaneous and of finite duration. I discuss slow dynamics that have been observed theoretically and experimentally for some quenches from the superfluid phase to the Mott insulating phase and the picture of two timescales, one for fast local equilibration and another for slow global equilibration, that appears to characterize this situation. I also discuss the theoretical and experimental observation of the Lieb-Robinson bounds for a variety of quenches and the Kibble-Zurek mechanism in quenches from the Mott insulator to superfluid. I conclude with a discussion of open questions and future directions.
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.