arXiv subjects

Khan W. Mahmud

Publications and source records attributed to Khan W. Mahmud.

7 recordsLinked to original sources

arXiv2018

Spin-orbit coupled bosons in one dimension: emergent gauge field and Lifshitz transition

In the presence of strong spin-independent interactions and spin-orbit coupling, we show that the spinor Bose liquid confined to one spatial dimension undergoes an interaction- or density-tuned quantum phase transition similar to one theoretically proposed for itinerant magnetic solid-state systems. The order parameter describes broken $Z_2$ inversion symmetry, with the ordered phase accompanied by non-vanishing momentum which is generated by fluctuations of an emergent dynamical gauge field at the phase transition. This quantum phase transition has dynamical critical exponent $z \simeq 2$, typical of a Lifshitz transition, but is described by a nontrivial interacting fixed point. From direct numerical simulation of the microscopic model, we extract previously unknown critical exponents for this fixed point. Our model describes a realistic situation of 1D ultracold atoms with Raman-induced spin-orbit coupling, establishing this system as a platform for studying exotic critical behavior of the Hertz-Millis type.

cond-mat.quant-gas↗

arXiv2018

Generalized Scene Reconstruction

A new passive approach called Generalized Scene Reconstruction (GSR) enables "generalized scenes" to be effectively reconstructed. Generalized scenes are defined to be "boundless" spaces that include non-Lambertian, partially transmissive, textureless and finely-structured matter. A new data structure called a plenoptic octree is introduced to enable efficient (database-like) light and matter field reconstruction in devices such as mobile phones, augmented reality (AR) glasses and drones. To satisfy threshold requirements for GSR accuracy, scenes are represented as systems of partially polarized light, radiometrically interacting with matter. To demonstrate GSR, a prototype imaging polarimeter is used to reconstruct (in generalized light fields) highly reflective, hail-damaged automobile body panels. Follow-on GSR experiments are described.

cs.CV↗

arXiv2016

Two coupled nonlinear cavities in a driven-dissipative environment

We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical analysis, we find steady-state solutions with different photon occupations in two cavities. Such states can be considered analogs of the closed system double well symmetry breaking states. We analyze the occurrence and properties of these localized states in the system parameter space and examine how the symmetry breaking states, in form of a bistable pair, are associated to the single cavity bistable behavior. In a full quantum calculation of the master equation dynamics that includes quantum fluctuations, the symmetry breaking states and bistability disappear due to the quantum fluctuations. In quantum trajectory picture, we observe enhanced quantum jumps and switching which indicate the presence of the underlying semiclassical symmetry breaking states. Finally, we present a set of analytical solutions for the steady state correlation functions using the complex P-representation and discuss its regime of validity.

quant-ph↗

arXiv2016

Collective phases of strongly interacting cavity photons

We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-$\frac{1}{2}$ model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

quant-ph↗

arXiv2011

Dynamical studies of macroscopic superposition states: Phase engineering of controlled entangled number states of Bose-Einstein condensate in multiple wells

We provide a scheme for the generation of entangled number states of Bose-Einstein condensates in multiple wells with cyclic pairwise connectivity. The condensate ground state in a multiple well trap can self-evolve, when phase engineered with specific initial phase differences between the neighboring wells, to a macroscopic superposition state with controllable entanglement -- to multiple well generalization of double well NOON states. We demonstrate through numerical simulations the creation of entangled states in three and four wells and then explore the creation of "larger" entangled states where there are either a larger number of particles in each well or a larger number of wells. The type of entanglement produced as the particle numbers, or interaction strength, increases changes in a novel and initially unexpected manner.

cond-mat.quant-gas↗

arXiv2005

Phase engineering of squeezed states and controlled entangled number states of Bose-Einstein condensates in multiple wells

We provide a scheme for the generation of controlled entangled number states of Bose-Einstein condensates in multiple wells, and also provide a novel method for the creation of squeezed states without severe adiabatic constraints on barrier heights. The condensate in a multiple well trap can be evolved, starting with a specific initial phase difference between the neighboring wells, to a tunable entangled state or a squeezed state. We propose a general formula for the initial phase difference between the neighboring wells that is valid for any number of wells, even and odd.

cond-mat.other↗

arXiv2004

Quantum phase space picture of Bose-Einstein Condensates in a double well: Proposals for creating macroscopic quantum superposition states and a study of quantum chaos

We present a quantum phase space model of Bose-Einstein condensate (BEC) in a double well potential. In a two-mode Fock-state analysis we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase space information is extracted from the stationary quantum states using the Husimi distribution function. It is shown that the quantum states are localized on the known classical phase space orbits of a nonrigid physical pendulum, and thus the novel phase space characteristics of a nonrigid physical pendulum such as the $π$ motions are seen to be a property of the exact quantum states. Low lying states are harmonic oscillator like libration states while the higher lying states are Schrödinger cat-like superpositions of two pendulum rotor states. To study the dynamics in phase space, a comparison is made between a displaced quantum wavepacket and the trajectories of a swarm of points in classical phase space. For a driven double well, it is shown that the classical chaotic dynamics is manifest in the dynamics of the quantum states pictured using the Husimi distribution. Phase space analogy also suggests that a $π$ phase displaced wavepacket put on the unstable fixed point on a separatrix will bifurcate to create a superposition of two pendulum rotor states - a Schrödinger cat state (number entangled state) for BEC. It is shown that the choice of initial barrier height and ramping, following a $π$ phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.

cond-mat.soft↗