arXiv subjects

K. W. Mahmud

Publications and source records attributed to K. W. Mahmud.

12 recordsLinked to original sources

arXiv2021

Manipulating atom-number distributions and detecting spatial distributions in lattice-confined spinor gases

We present an experimental study demonstrating the manipulation of atom-number distributions of spinor gases after nonequilibrium quantum quenches across superfluid to Mott-insulator phase transitions in cubic optical lattices. Our data indicate that atom distributions in individual Mott lobes can be tuned by properly designing quantum quench sequences, which suggests methods of maximizing the fraction of atoms in Mott lobes of even occupation numbers and has applications in attaining different quantum magnetic phases including massively entangled states. Spatial distributions of gases in three-dimensional lattices are derived from the observed number distributions, which reveal complex spatial dynamics during the quantum quenches. Qualitative agreements are also found between our experimental data and numerical simulations based on time-dependent Gutzwiller approximations in two-dimensional systems.

cond-mat.quant-gas↗

arXiv2020

Quantum critical dynamics in a spinor Hubbard model quantum simulator

Three-dimensional (3D) strongly correlated many-body systems, especially their dynamics across quantum phase transitions, are prohibitively difficult to be numerically simulated. We experimentally demonstrate that such complex many-body dynamics can be efficiently studied in a 3D spinor Bose-Hubbard model quantum simulator, consisting of antiferromagnetic spinor Bose-Einstein condensates confined in cubic optical lattices. We find novel dynamics and scaling effects beyond the scope of existing theories at superfluid-insulator quantum phase transitions and highlight spin populations as a new observable to probe the quantum critical dynamics. Our data indicate that the scaling exponents are independent of the nature of the quantum phase transitions. We also conduct numerical simulations in lower dimensions using time-dependent Gutzwiller approximations, which qualitatively describe our observations.

cond-mat.quant-gas↗

arXiv2014

Dynamically decoupled three-body interactions with applications to interaction-based quantum metrology

We propose a stroboscopic method to dynamically decouple the effects of two-body atom-atom interactions for ultracold atoms, and realize a system dominated by elastic three-body interactions. Using this method, we show that it is possible to achieve the optimal scaling behavior predicted for interaction-based quantum metrology with three-body interactions. Specifically, we show that for ultracold atoms quenched in an optical lattice, we can measure the three-body interaction strength with a precision proportional to ${\bar n}^{-5/2}$ using homodyne quadrature interferometry, and ${\bar n}^{-7/4}$ using conventional collapse-and-revival techniques, where ${\bar n}$ is the mean number of atoms per lattice site. Both precision scalings surpass the nonlinear scaling of ${\bar n}^{-3/2}$, the best so far achieved or proposed with a physical system. Our method of achieving a decoupled three-body interacting system may also have applications in the creation of exotic three-body states and phases.

cond-mat.quant-gas↗

arXiv2014

Particle-Hole Pair Coherence in Mott Insulator Quench Dynamics

We predict the existence of novel collapse and revival oscillations that are a distinctive signature of the short-range off-diagonal coherence associated with particle-hole pairs in Mott insulator states. Starting with an atomic Mott state in a one-dimensional optical lattice, suddenly raising the lattice depth freezes the particle-hole pairs in place and induces phase oscillations. The peak of the quasi-momentum distribution, revealed through time of flight interference, oscillates between a maximum occupation at zero quasi-momentum (the $Γ$ point) and the edge of the Brillouin zone. We show that the population enhancements at the edge of the Brillouin zone is due to coherent particle-hole pairs, and we find similar effects for fermions and Bose-Fermi mixtures in a lattice. Our results open a new avenue for probing strongly correlated many-body states with short-range phase coherence that goes beyond the familiar collapse and revivals previously observed in the long-range coherent superfluid regime.

cond-mat.quant-gas↗

arXiv2013

Bloch oscillations and quench dynamics of interacting bosons in an optical lattice

We study the dynamics of interacting superfluid bosons in a one dimensional vertical optical lattice after a sudden increase of the lattice potential depth. We show that this system can be exploited to investigate the effects of strong interactions on Bloch oscillations. We perform theoretical modelling of this system, identify experimental challenges and explore a new regime of Bloch oscillations characterized by interaction-induced matter-wave collapse and revivals which modify the Bloch oscillations dynamics. In addition, we study three dephasing mechanisms: effective three-body interactions, finite value of tunneling, and a background harmonic potential. We also find that the center of mass motion in the presence of finite tunneling goes through collapse and revivals, giving an example of quantum transport where interaction induced revivals are important. We quantify the effects of residual harmonic trapping on the momentum distribution dynamics and show the occurrence of interaction-modified temporal Talbot effect. Finally, we analyze the prospects and challenges of exploiting Bloch oscillations of cold atoms in the strongly interacting regime for precision measurement of the gravitational acceleration $g$.

cond-mat.quant-gas↗

arXiv2013

Dynamics of spin-1 bosons in an optical lattice: spin mixing, quantum phase revival spectroscopy and effective three-body interactions

We study the dynamics of spin-1 atoms in a periodic optical-lattice potential and an external magnetic field in a quantum quench scenario where we start from a superfluid ground state in a shallow lattice potential and suddenly raise the lattice depth. The time evolution of the non-equilibrium state, thus created, shows collective collapse-and-revival oscillations of matter-wave coherence as well as oscillations in the spin populations. We show that the complex pattern of these two types of oscillations reveals details about the superfluid and magnetic properties of the initial many-body ground state. Furthermore, we show that the strengths of the spin-dependent and spin-independent atom-atom interactions can be deduced from the observations. The Hamiltonian that describes the physics of the final deep lattice not only contains two-body interactions but also effective multi-body interactions, which arise due to virtual excitations to higher bands. We derive these effective spin-dependent three-body interaction parameters for spin-1 atoms and describe how spin-mixing is affected. Spinor atoms are unique in the sense that multi-body interactions are directly evident in the in-situ number densities in addition to the momentum distributions. We treat both antiferromagnetic (e.g. $^{23}$Na atoms) and ferromagnetic (e.g. $^{87}$Rb and $^{41}$K) condensates.

cond-mat.quant-gas↗

arXiv2011

Finite temperature study of bosons in a two dimensional optical lattice

We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two dimensional optical lattice. The scale invariant, finite temperature, state diagram is presented for the Bose-Hubbard model in terms of experimental parameters -- the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott Insulator and normal Bose liquid phases, we examine the local density, compressibility, superfluid density and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between 1D and 2D, while at finite temperature, the decay is similar to that in 1D at a much lower temperature. The calculations reveal shortcomings of the local density approximation (LDA) in describing superfluid properties of trapped bosons. We also present the finite temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite temperature effect in the experiment.

cond-mat.quant-gas↗

arXiv2010

Isentropes of spin-1 bosons in an optical lattice

We analyze the effects of adiabatic ramping of optical lattices on the temperature of spin-1 bosons in a homogeneous lattice. Using mean-field theory, we present the isentropes in the temperature-interaction strength ($T,U_0$) plane for ferromagnetic, antiferromagnetic, and zero spin couplings. Following the isentropic lines, temperature changes can be determined during adiabatic loading of current experiments. We show that the heating-cooling separatrix lies on the superfluid-Mott phase boundary with cooling occuring within the superfluid and heating in the Mott insulator, and quantify the effects of spin coupling on the heating rate. We find that the mean-field isentropes for low initial entropy terminate at the superfluid-Mott insulator phase boundary.

cond-mat.quant-gas↗

arXiv2008

Canonical Trajectories and Critical Coupling of the Bose-Hubbard Hamiltonian in a Harmonic Trap

Quantum Monte Carlo (QMC) simulations and the Local Density Approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose Hubbard Hamiltonian confined in a harmonic trap onto the $(μ/U,t/U)$ phase diagram of the uniform system. Generically, these curves do not intercept the tips of the Mott insulator (MI) lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results.

cond-mat.other↗

arXiv2003

Phase engineering of controlled entangled number states in a single component Bose-Einstein condensate in a double well

We propose a model for the creation of entangled number states (Schrödinger cat states) of a Bose-Einstein condensate in a double well through simple phase engineering. We show that a $π$-phase imprinted condensate in a double-well evolves, with a simultaneous change of barrier height, to number states with well defined and controlled entanglement. The cat state generation is understood in terms of the underlying classical phase space dynamics of a $π$-phase displaced coherent state put at the hyperbolic fixed point of the separatrix of a physical pendulum. The extremity and sharpness of the final cat state is determined by the initial barrier height and the rate at which it is ramped during the evolution.

cond-mat↗

arXiv2003

Bose-Einstein condensates in a one-dimensional double square well: Analytical solutions of the Nonlinear Schrödinger equation and tunneling splittings

We present a representative set of analytic stationary state solutions of the Nonlinear Schrödinger equation for a symmetric double square well potential for both attractive and repulsive nonlinearity. In addition to the usual symmetry preserving even and odd states, nonlinearity introduces quite exotic symmetry breaking solutions - among them are trains of solitons with different number and sizes of density lumps in the two wells. We use the symmetry breaking localized solutions to form macroscopic quantum superpositions states and explore a simple model for the exponentially small tunneling splitting.

cond-mat↗

arXiv2001

Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth

The fundamental question of how Bose-Einstein condensates tunnel into a barrier is addressed. The cubic nonlinear Schrodinger equation with a finite square well potential, which models a Bose-Einstein condensate in a quasi-one-dimensional trap of finite depth, is solved for the complete set of localized and partially localized stationary states, which the former evolve into when the nonlinearity is increased. An immediate application of these different solution types is tunable tunneling. Magnetically tunable Feshbach resonances can change the scattering length of certain Bose-condensed atoms, such as $^{85}$Rb, by several orders of magnitude, including the sign, and thereby also change the mean field nonlinearity term of the equation and the tunneling of the wavefunction. We find both linear-type localized solutions and uniquely nonlinear partially localized solutions where the tails of the wavefunction become nonzero at infinity when the nonlinearity increases. The tunneling of the wavefunction into the non-classical regime and thus its localization therefore becomes an external experimentally controllable parameter.

cond-mat↗