Session Z45: Bose-Einstein Condensates, Matter Optics, and Atomic Interferometry

New Facility to Probe Physics With Degenerate Bose and Fermi Gas

A new facility to produce dual species degenerate Bose and Fermi gas is under construction at JQI. This apparatus is designed to create degnerate mixtures of bosonic rubidium ($^{87}$Rb) and fermionic lithium ($^{6}$Li). A degenerate Bose-Fermi mixture supports many quantum phase transitions, giving an experimental platform to study many-body statics, dynamics, and perhaps precision measurements. High T$_c$ superconductivity could be probed, where fermions are bound into Cooper pairs by boson mediated interactions. Dual species heteronuclear molecules with large permanent electric dipole moment may lead to a system for implementing quantum bits. A spin-polarized, non-interacting, degenerate $^{6}$Li gas coupled to $^{87}$Rb atoms in an optical lattice will give rise to a long range, spin-dependent interactions to realize quantum magnetism and potentially supersolidity. Far red-detuned lattices are far weaker, in recoil units, for Li as compared to Rb. So, in the Mott phase of Rb - one atom per lattice site - the three body recombination of Li-Li-Rb is greatly suppressed. Thus the wide $^{87}$Rb-$^{6}$Li Fesbach resonance at 1.1 kG is expected to effectively control fermion mediated interactions.   

Solitons and Breathers in Strongly Repulsive Bose-Einstein Condensates

Collisional dynamics of solitary matter waves of hard core bosons, consisting of dark and bright waves as well as supersonic periodic trains, reveals remarkable richness and coherence, with the phase of the condensate playing a key role. Depending upon the condensate density, we see two distinctive effects in the collision of these waves: intuitively expected repulsive collision due to hard core boson constraint and also collisions in which they ``pass through'' each other without distortion. In addition to confirming the soliton status of the solitary waves, our studies reveal a variety of multi-solitons including a family of breathers, that can be demonstrated in an optical lattice with appropriate phase imprinting.   

Macroscopic two-state systems in trapped atomic condensates

We consider a macroscopic two-sate system based on persistent current states of a Bose-Einstein condensate (BEC) of interacting neutral atoms confined in a ring with a weak Josephson link [1]. We demonstrate that macroscopic superpositions of different BEC flows are energetically favorable in this system. Moreover, a macroscopic two-state dynamics emerges in the low energy limit. We also investigate fundamental limitations due to the noise inherent to the interacting BEC of Josephson-ring geometry. We show that the coherent macroscopic dynamics is readily measurable for an experimentally accessible range of parameters. \\[4pt] [1] D. Solenov and D. Mozyrsky, arXiv:1009.1901 [cond-mat.quant-gas].   

Analysis of a free oscillation atom interferometer

We analyze a Bose-Einstein condensate (BEC) - based free oscillation atom Michelson interferometer in a weakly confining harmonic magnetic trap. A BEC at the center of the trap is split into two harmonics by a laser standing wave. The harmonics move in opposite directions with equal speeds and return under the influence of the trapping potential at their classical turning points. The harmonics are allowed to pass through each other and a recombination pulse is applied when they overlap at the end of a cycle after their return at the second time. We derive an expression for the contrast of the interferometric fringes and obtain the fundamental limit of performance of the interferometer in the parameter space. The results are also compared and contrasted with the results of our previous work on a single- and double reflection atom Michelson interferometers.   

Atomic population distribution in the output ports of a waveguide interferometer with optical splitting and recombination

Manipulation of atomic Bose-Einstein condensates (BECs) in an atom waveguide interferometer relies on the use of off-resonant laser pulses to split a cloud of BEC into two clouds that travel along different paths and are then recombined using the same laser pulses. During the evolution of the condensates, residual spatial-dependent phase is accumulated due to the confining potential and the inter-atomic interactions within the condensates. Additional phase is accumulated due to the mode-entangled state of the clouds after splitting that causes each atom in the condensate to evolve at a different rate. The recombination laser pulses are sensitive to these phases and the population of atoms in the atomic samples that emerge after recombination depends on them. We derive an expression for the probability density distribution of observing any number of atoms in the clouds after recombination and give a parameter space for optimum operation of the interferometer in the presence of phase due to mode-entangled state of BEC clouds and the residual spatial-dependent phase.   

Momentum-space engineering of gaseous Bose-Einstein condensates

We show how the momentum distribution of gaseous Bose--Einstein condensates can be shaped by applying a sequence of standing--wave laser pulses. We present a theory, whose validity was demonstrated in an earlier experiment,\footnote{L.\ Deng, et al., PRL {\bf 83}, 5407 (1999)} of the effect of a two--pulse sequence on the condensate wavefunction in momentum space. We generalize the previous result to the case of $N$ pulses having arbitrary pulse areas and separated by arbitrary time intervals and show how these parameters can be engineered to produce a desired final momentum distribution. We find that several momentum distributions, such as single--state distributions or a range of momentum states which are important in initial state selection in atom--interferometry applications, can be engineered with high fidelity with two or three pulses. We present several examples of such distributions and show how the fidelity improves as more pulses are added. We also give some ideas of how these momentum distributions can be applied to atom interferometry.   

Enhanced atom interferometry through quantum information science

New designs for atom interferometers can be inspired by quantum information science (QIS). QIS--inspired atom interferometer (AI) designs have the potential for producing AIs with enhanced sensitivity and robustness. We compare the sensitivity of a standard Mach--Zehnder (M--Z) Bragg AI with an AI whose design is based on the idea of decoherence--free subspaces (DFS).\footnote{D.A.\ Pushin, M.\ Arif, and D.G.\ Cory, Phys.Rev.\ A {\bf 79}, 053635 (2009)} We studied the performance of both atom interferometers using an enhanced version of a previously developed Bragg interferometer prototyping model.\footnote{S.E.\ Simsarian et al., Phys.\ Rev.Lett.\ {\bf 85}, 2040 (2000).} This model approximates the effect on the condensate of multiple Bragg pulses separated by time delays using two elements: the effect of a single pulse and condensate evolution between pulses. The overall effect is rapidly approximated by following the steps of the interferometric process. We describe this model and then present the comparison of the performance of the M--Z interferometer with that of the DFS--inspired interferometer.   

Eigenvalues of the linearized collision operator for a Bose-condensed gas

Beginning from a Hamiltonian description, we have derived the kinetic equation for the elementary excitations of an interacting gas of bosons with and without a condensate. This kinetic equation is the quantum analog of the Boltzmann equation for a classical gas. Linearizing the kinetic equation about the equilibrium state allows us to treat it as a linear integral operator equation and find its eigenvalues. These eigenvalues give the rates at which different eigenmodes relax to equilibrium. They also provide a relationship between the microscopic properties of the interacting particles and the macroscopic properties of the gas.   

Single-Particle Spectral Density of a Bose-Condensed Gas in the Two-Fluid Hydrodynamic Regime

In Bose supefluids, the single-particle Green's function can be directly related to the superfluid velocity-velocity correlation function in the hydrodynamic regime. An explicit expression for the single-particle spectral density was originally written down by Hohenberg and Martin in 1965, starting from the two-fluid equations for a superfluid. We give a new simple derivation of their results. Using these results, we calculate the relative weights of first and second sound modes in the single-particle spectral density as a function of temperature in a uniform Bose gas. We show that the second sound mode makes a dominant contribution to the single-particle spectrum in relatively high temperature region. We also discuss the possibility of experimental observation of the second sound mode In a Bose gas by photoemission spectroscopy.   

A new self-consistent perturbation expansion for Bose-Einstein condensates satisfying conservation laws and Goldstone's theorem

Quantum-field-theoretic descriptions of Bose-Einstein condensates (BEC) have suffered from the lack of self-consistent approximation schemes satisfying Goldstone's theorem and dynamical conservation laws simultaneously. I will report on a new perturbation expansion of the kind developed recently and its predictions on the single-particle and two-particle excitations of BEC. It is shown that the single-particle Bogoliubov excitations are generally different from the two-particle density fluctuations in contradiction to the conclusion of previous studies. I will elucidate some properties of the two distinct modes in connection with Goldstone's theorem on spontaneously broken symmetries. References: T. Kita, Phys. Rev. B80, 214502 (2009); Phys. Rev. B81, 214513 (2010).   

Hamiltonian monodromy in the spectrum and dynamics of a spin-1 Bose condensate

A spin-1 Bose condensate in a magnetic field in the single mode approximation -- valid for sufficiently small condensates -- represents a rather simple dynamical system. In this talk I will show that there is nevertheless scope for some rather unusual behavior. In particular, this system displays the phenomenon of \emph{Hamiltonian monodromy}, a topological obstruction to the existence of global action-angle variables. I will discuss the signatures of this phenomenon in the classical dynamics and quantum spectrum   

Ground States of a Mixture of Two Species of Spinor Bose Gases with Interspecies Spin Exchange

We consider a mixture of two species of spin-1 atoms with both interspecies and intraspecies spin exchanges, and find out the exact ground states in various parameter regimes. We describe the quantum phase diagrams in the space of parameters, including intraspecies and interspecies spin coupling strengths as well as the magnetic field. The boundaries where the ground states are either continuous or discontinuous are determined, with the latter identified as where quantum phase transitions take place. Interspecies spin exchange leads to features beyond the usual ones of a single species of spinor atoms.   

Bound states of a localized magnetic impurity in a superfluid of paired ultracold fermions

The nature of states formed around localized impurities can be a valuable probe of the properties of a quantum many body system. We propose using a deep optical lattice to localize an impurity atoms. We show that such and impurity atom acts like a magnetic impurity and leads to the formation of a pair of Shiba bound states inside the superconducting gap as well as possible bound states below the Fermi. The properties of these localized bound states can be read out using RF spectroscopy.   

Spectroscopy for cold atom gases in periodically modulated optical lattice potential

Cold atoms in optical lattices are vigorously studied experimentally and theoretically as one of the candidates for a quantum simulator. At the same time, further development of probes to microscopic structure of systems is needed. We propose a novel spectroscopy in cold atom experiments by use of periodic phase-modulation of optical lattice potentials. Corresponding to the statistics of atoms, we formulate the different observables: The energy absorption rate for bosonic atom gases, and the doublon production rate for fermionic atom gases. These observables are formulated within the linear response theory. Interestingly they are given by the imaginary part of the retarded current-current correlation function which is familiar as a quantity corresponding to an optical conductivity. As an example, we discuss one-dimensional Mott insulating state, and also compare our spectroscopy with another known spectroscopy by amplitude-modulation of an optical lattice.   

Subwavelength localization of a single atom via resonance fluorescence photon statistics

A subwavelength localization scheme of a single atom is investigated. The localization is based on the interaction of the two-level atom with a standing wave laser field. The photon statistics of resonant fluorescence depends on the Rabi frequency of the driving laser field and thus the position of the atom inside the standing wave. We show that this dependence can be used to localize the atom to a subwavelength accuracy.