Thomás Fogarty

Quenching small quantum gases: Genesis of the orthogonality catastrophe

We study the dynamics of two strongly interacting bosons with an additional impurity atom trapped in a harmonic potential. Using exact numerical diagonalization we are able to fully explore the dynamical evolution when the interaction between the two distinct species is suddenly switched on (quenched). We examine the behavior of the densities, the entanglement, the Loschmidt echo and the spectral function for a large range of inter-species interactions and find that even in such small systems evidence of Andersons orthogonality catastrophe can be witnessed.

Orthogonality catastrophe as a consequence of qubit embedding in an ultracold Fermi gas

We investigate the behavior of a two-level atom coupled to a one-dimensional, ultracold Fermi gas. The sudden switching on of the scattering between the two entities leads to the loss of any coherence in the initial state of the impurity and we show that the exact dynamics of this process is strongly influenced by the effect of the orthogonality catastrophe within the gas. We highlight the relationship between the Loschmidt echo and the retarded Greens function - typically used to formulate the dynamical theory of the catastrophe - and demonstrate that the effect is reflected in the impurity dynamics. We show that the expected nonexponential decay of the spectral function can be observed using Ramsey interferometry on the two-level atom and comment on finite temperature effects.

Dynamical phase transitions, temporal orthogonality and the dynamics of observables in one dimensional ultra-cold quantum gases: from the continuum to the lattice

Classical constraints on the reduced density matrix of quantum fluids in a single Landau level, termed as local exclusion conditions (LECs) [B. Yang, arXiv:1901.00047], have recently been shown to characterize the ground state of many FQH phases. In this work, we extend the LEC construction to build the elementary excitations, namely quasiholes and quasielectrons, of these FQH phases. In particular, we elucidate the quasihole counting, categorize various types of quasielectrons, and construct their microscopic wave functions. Our extensive numerical calculations indicate that the undressed quasielectron excitations of the Laughlin state obtained from LECs are topologically equivalent to those obtained from the composite fermion theory. Intriguingly, the LEC construction unveils interesting connections between different FQH phases and offers a novel perspective on exotic states such as the Gaffnian and the Fibonacci state.We investigate the dynamics of the rate function and of local observables after a quench in models which exhibit phase transitions between a superfluid and an insulator in their ground states. Zeros of the return probability, corresponding to singularities of the rate functions, have been suggested to indicate the emergence of dynamical criticality and we address the question of whether such zeros can be tied to the dynamics of physically relevant observables and hence order parameters in the systems. For this we first numerically analyze the dynamics of a hard-core boson gas in a one-dimensional waveguide when a quenched lattice potential is commensurate with the particle density. Such a system can undergo a pinning transition to an insulating state and we find non-analytic behavior in the evolution of the rate function which is indicative of dynamical phase transitions. In addition, we perform simulations of the time dependence of the momentum distribution and compare the periodicity of this collapse and revival cycle to that of the non-analyticities in the rate function: the two are found to be closely related only for deep quenches. We then confirm this observation by analytic calculations on a closely related discrete model of hard-core bosons in the presence of a staggered potential and find expressions for the rate function for the quenches. By extraction of the zeros of the Loschmidt amplitude we uncover a non-equilibrium timescale for the emergence of non-analyticities and discuss its relationship with the dynamics of the experimentally relevant parity operator.

Non-equilibrium thermodynamics of harmonically trapped bosons

We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with strong interactions after a quench and we find its occurrence analytically for an infinitely repulsive pair of atoms. We further show this phenomena is related to the fundamental excitations that dictate the dynamics from the spectral function. We establish a clear qualitative link between the amount of (irreversible) work performed on the system and the establishment of entanglement. We extend our analysis to multipartite systems by examining the case of three trapped atoms. We show the initial (pre-quench) interactions play a vital role in determining the dynamical features, while the qualitative features of the two particle case appear to remain valid. Finally, we propose the use of the atomic density profile as a readily accessible indicator of the non-equilibrium properties of the systems in question.

Localization transition in the presence of cavity backaction

We study the localization transition of an atom confined by an external optical lattice in a high-finesse cavity. The atom-cavity coupling yields an effective secondary lattice potential, whose wavelength is incommensurate with the periodicity of the optical lattice. The cavity lattice can induce localization of the atomic wave function analogously to the Aubry-Andre localization transition. Starting from the master equation for the cavity and the atom we perform a mapping of the system dynamics to a Hubbard Hamiltonian, which can be reduced to the Harpers Hamiltonian in appropriate limits. We evaluate the phase diagram for the atom ground state and show that the transition between extended and localized wavefunction is controlled by the strength of the cavity nonlinearity, which determines the size of the localized region and the behaviour of the Lyapunov exponent. The Lyapunov exponent, in particular, exhibits resonance-like behaviour in correspondence with the optomechanical resonances. Finally we discuss the experimental feasibility of these predictions.

Entangling two defects via a surrounding crystal

Bundesministerium fur Bildung und Forschung (QuOREp); Irish Research Council (Embark Initiative (RS/2009/1082)

An efficient nonlinear Feshbach engine

We investigate a thermodynamic cycle using a Bose-Einstein condensate with nonlinear interactions as the working medium. Exploiting Feshbach resonances to change the interaction strength of the BEC allows us to produce work by expanding and compressing the gas. To ensure a large power output from this engine these strokes must be performed on a short timescale, however such non-adiabatic strokes can create irreversible work which degrades the engines efficiency. To combat this, we design a shortcut to adiabaticity which can achieve an adiabatic-like evolution within a finite time, therefore significantly reducing the out-of-equilibrium excitations in the BEC. We investigate the effect of the shortcut to adiabaticity on the efficiency and power output of the engine and show that the tunable nonlinearity strength, modulated by Feshbach resonances, serves as a useful tool to enhance the systems performance.

Optomechanics with a position-modulated Kerr-type nonlinear coupling

Cavity optomechanics has proven to be a field of research rich with possibilities for studying motional cooling, squeezing, quantum entanglement and metrology in solid state systems. While to date most studies have focused on the modulation of the cavity frequency by the moving element, the emergence of new materials will soon allow to explore the influences of nonlinear optical effects. We therefore study in this work the effects due to a nonlinear position-modulated self-Kerr interaction and find that this leads to an effective coupling that scales with the square of the photon number, meaning that significant effects appear even for very small nonlinearities. This strong effective coupling can lead to lower powers required for motional cooling and the appearance of multi-stability in certain regimes.

An eccentrically perturbed Tonks?Girardeau gas

We investigate the static and dynamic properties of a Tonks?Girardeau gas in a harmonic trap with an eccentric ?-perturbation of variable strength. For this, we first find the analytic eigensolution of the single particle problem and then use this solution to calculate the spatial density and energy profiles of the many-particle gas as a function of the strength and position of the perturbation. We find that the crystal nature of the Tonks state is reflected in both the lowest occupation number and the momentum distribution of the gas. As a novel application of our model, we study the time evolution of the spatial density after the sudden removal of the perturbation. The dynamics exhibits collapses and revivals of the original density distribution, which occur in units of the trap frequency. This is reminiscent of the Talbot effect from classical optics.

Probing the out-of-equilibrium dynamics of two interacting atoms

We study the out-of-equilibrium dynamics of two interacting atoms in a one-dimensional harmonic trap after a quench by a tightly pinned impurity atom. We make use of an approximate variational calculation called the Lagrange-mesh method to solve the Schrodinger equation as a function of inter-particle interaction and impurity quench strength. We investigate the out-of-equilibrium dynamics by calculating the Loschmidt echo which quantifies the irreversibility of the system following the quench, while its probability distribution after long times can be used to identify distinct dynamical regimes. These quantities are related to the spectral function which describes the full dynamical spectrum, and we show through a thorough examination of the parameter space the existence of distinct scattering states and collective oscillations. This work demonstrates how these dynamics are strongly dependent on the interaction strength between the atoms and may be tuned to reach the orthogonality catastrophe in few-body systems.