Kunal K. Das

Bose-Fermi mixtures in one dimension

We analyze the phase stability and the response of a mixture of bosons and spin-polarized fermions in one dimension (1D). Unlike in 3D, phase separation happens for low fermion densities. The dynamics of the mixture at low energy is independent of the spin-statistics of the components, and the modes are essentially undamped.

Quantum Pumping with Ultracold Atoms on Microchips: Fermions versus Bosons

We present a design for simulating quantum pumping of electrons in a mesoscopic circuit with ultracold atoms in a micromagnetic chip trap. We calculate theoretical results for quantum pumping of both bosons and fermions, identifying differences and common features, including geometric behavior and resonance transmission. We analyze the feasibility of experiments with bosonic ;{87}Rb and fermionic ;{40}K atoms with an emphasis on reliable atomic current measurements.

Highly anisotropic Bose-Einstein condensates: Crossover to lower dimensionality

We develop a simple analytical model based on a variational method to explain the properties of trapped cylindrically symmetric Bose-Einstein condensates of varying degrees of anisotropy, well into the regimes of effective one dimension and effective two dimensions. Our results are accurate in regimes where the Thomas-Fermi approximation breaks down and they are shown to be in agreement with recent experimental data. We also present analytic expressions for various ground-state properties and quasiparticle excitations valid for highly anisotropic condensates.

Thermodynamic and noise considerations for the detection of microscopic particles in a gas by Photoacoustic Raman spectroscopy

We develop a simple thermodynamic model to describe the heat transfer mechanisms and generation of acoustic waves in photoacoustic Raman spectroscopy by small particulate suspensions in a gas. Using Langevin methods to describe the thermal noise we study the signal and noise properties, and from the noise equivalent power we determine the minimum number density of the suspended particles that can be detected. We find that for some relevant cases, as few as 100 particles per cubic meter can be detected.

Interference of a thermal tonks gas on a ring

A nonzero temperature generalization of the Fermi-Bose mapping theorem is used to study the exact quantum statistical dynamics of a one-dimensional gas of impenetrable bosons on a ring. We investigate the interference produced when an initially trapped gas localized on one side of the ring is released, split via an optical-dipole grating, and recombined on the other side of the ring. Nonzero temperature is shown not to be a limitation to obtaining high visibility fringes.

Crossover from one to three dimensions for a gas of hard-core bosons.

We develop a variational theory of the crossover from the one-dimensional (1D) regime to the 3D regime for ultracold Bose gases in thin waveguides. Within the 1D regime we map out the parameter space for fermionization, which may span the full 1D regime for suitable transverse confinement.

Theory of a one-dimensional double-X-junction atom interferometer

The dynamics of an atom waveguide X-junction beam splitter becomes truly one dimensional in a regime of low temperatures and densities and large positive scattering lengths where the transverse mode becomes frozen and themany-body Schrodinger dynamics becomes exactly soluble via a generalized Fermi-Bose mapping theorem. We analyze the interferometric response of a double-X-junction interferometer of this type due to potential differences between the interferometer arms.

Controlled flow of spin-entangled electrons via adiabatic quantum pumping.

We propose a method to dynamically generate and control the flow of spin-entangled electrons, each belonging to a spin singlet, by means of adiabatic quantum pumping. The pumping cycle functions by periodic time variation of localized two-body interactions. We develop a generalized approach to adiabatic quantum pumping as traditional methods based on a scattering matrix in one dimension cannot be applied here. We specifically compute the flow of spin-entangled electrons within a Hubbard-like model of quantum dots, discuss possible implementations, and identify parameters that can be used to control the singlet flow.

Spin squeezing by tensor twisting and Lipkin-Meshkov-Glick dynamics in a toroidal Bose-Einstein condensate with spatially modulated nonlinearity

We propose a scheme for spin-squeezing in the orbital motion of a Bose-Einstein condensate (BEC) in a toroidal trap. A circular lattice couples two counter-rotating modes and squeezing is generated by the nonlinear interaction spatially modulated at half the lattice period. By varying the amplitude and phase of the modulation, various cases of the twisting tensor can be directly realized, leading to different squeezing regimes. These include one-axis twisting and the two-axis counter-twisting which are often discussed as the most important paradigms for spin squeezing. Our scheme naturally realizes the Lipkin-Meshkov-Glick model with the freedom to vary all its parameters simultaneously.

Time limited optimal dynamics beyond the Quantum Speed Limit

The quantum speed limit sets the minimum time required to transfer a quantum system completely into a given target state. At shorter times the higher operation speed has to be paid with a loss of fidelity. Here we quantify the trade-off between the fidelity and the duration in a system driven by a time-varying control. The problem is addressed in the framework of Hilbert space geometry offering an intuitive interpretation of optimal control algorithms. This approach is applied to non-uniform time variations which leads to a necessary criterion for control optimality applicable as a measure of algorithm convergence. The time fidelity trade-off expressed in terms of the direct Hilbert velocity provides a robust prediction of the quantum speed limit and allows to adapt the control optimization such that it yields a predefined fidelity. The results are verified numerically in a multilevel system with a constrained Hamiltonian, and a classification scheme for the control sequences is proposed based on their optimizability.