arXiv subjects

J. Mumford

Publications and source records attributed to J. Mumford.

15 recordsLinked to original sources

arXiv2026

Topologically protected Bell-cat states in a simple spin model

We consider the topological properties of the so-called central spin model that consists of $N$ identical spins coupled to a single distinguishable central spin which arises in physical systems such as circuit-QED and bosonic Josephson junctions coupled to an impurity atom. The model closely corresponds to the Su-Schrieffer-Heeger (SSH) model except that the chain of sites in the SSH model is replaced by a chain of states in Fock space specifying the magnetization. We find that the model accommodates topologically protected eigenstates that are `Bell-cat' states consisting of a Schrödinger cat state of the $N$ spins that is maximally entangled with the central spin, and show how this state can be adiabatically created and moved along the chain by driving the central spin. The Bell-cat states are visualized by plotting their Wigner function and we explore their robustness against random noise by solving the master equation for the density matrix. We also explain the essential topological difference between identical spins and the excitations of a bosonic mode.

quant-ph↗

arXiv2025

Universal Long-Time Behavior of the Quantum Fisher Information in Dynamical Quantum Phase Transitions

We investigate dynamical quantum phase transitions (DQPTs) in quantum systems that possess well-defined classical limits, focusing on the spinor Bose-Einstein condensate and the Lipkin-Meshkov-Glick model. We diagnose the DQPTs with the long-time average of the quantum Fisher information (QFI) showing that it abruptly changes at the transition point. Using mean-field and semiclassical approximations, we demonstrate that the long-time average of the QFI reveals universal behavior that persists across different systems.

quant-ph↗

arXiv2025

Characterizing the transition from topology to chaos in a kicked quantum system

This work theoretically investigates the transition from topology to chaos in a periodically driven system consisting of a quantum top coupled to a spin-1/2 particle. The system is driven by two alternating interaction kicks per period. For small kick strengths, localized topologically protected bound states exist, and as the kick strengths increase, these states proliferate. However, at large kick strengths they gradually delocalize in stages, eventually becoming random orthonormal vectors as chaos emerges. We identify the delocalization of the bound states as a finite size effect where their proliferation leads to their eventual overlap. This insight allows us to make analytic predictions for the onset and full emergence of chaos which are supported by numerical results of the quasi-energy level spacing ratio and Rényi entropy. A dynamical probe is also proposed to distinguish chaotic from regular behavior.

quant-ph↗

arXiv2024

Gauge potentials and vortices in the Fock space of a pair of periodically driven Bose-Einstein condensates

We perform a theoretical study of the coupled dynamics of two species of Bose-Einstein condensates (BECs) in a double well potential where both the tunneling and the interatomic interactions are driven periodically in time. The population difference between the wells of each species gives rise to a two dimensional lattice in Fock space with dimensions given by the number of atoms in each BEC. We use a Floquet analysis to derive an effective Hamiltonian that acts in this Fock space and find that it contains an artificial gauge field. This system simulates noninteracting particles in a tight binding lattice subject to an additional harmonic potential and vector potential. When the intra-species interactions are attractive there is a critical value at which the ground state of the Floquet operator undergoes a transition from a Gaussian state to a quantized vortex state in Fock space. The transition can be quantified in terms of the angular momentum as well as the entanglement entropy of the ground state with both showing sudden jumps as the intra-species interactions become stronger. The stability of the vortex state vanishes in the thermodynamic limit.

cond-mat.quant-gas↗

arXiv2023

Many topological regions on the Bloch sphere of the spin-1/2 double kicked top

Floquet topological systems have been shown to exhibit features not commonly found in conventional topological systems such as topological phases characterized by arbitrarily large winding numbers. This is clearly highlighted in the quantum double kicked rotor coupled to spin-1/2 degrees of freedom [Phys. Rev. A 97, 063603 (2018)] where large winding numbers are achieved by tuning the kick strengths. Here, we extend the results to the spin-1/2 quantum double kicked top and find not only does the system exhibit topological regions with large winding numbers, but a large number of them are needed to fully characterize the topology of the Bloch sphere of the top for general kick strengths. Due to the geometry of the Bloch sphere it is partitioned into regions with different topology and the boundaries separating them are home to 0 and $π$ quasienergy bound states. We characterize the regions by comparing local versions of the mean field, quantum and mean chiral displacement winding numbers. We also use a probe state to locate the boundaries by observing localization as the state evolves when it has a large initial overlap with bound states. Finally, we briefly discuss the connections between the spin-1/2 quantum double kicked top and multi-step quantum walks, putting the system in the context of some current experiments in the exploration of topological phases.

quant-ph↗

arXiv2022

Two-particle topological Thouless spin pump

We show that two particles interacting via spin exchange exhibit topological features found in one-dimensional single particle lattice models. This is accomplished by absorbing all of the spatial degrees of freedom of the lattices into the spin degrees of freedom of the two particles. Comparing the spin system with the Su-Schrieffer-Heeger model, we show the existence of topologically protected edge spin states and establish the bulk-edge correspondence. Modifying the spin system with a chiral symmetry breaking term results in it resembling the Rice-Mele model and can therefore act as a Thouless spin pump of one of the particles when periodically and adiabatically driven. By using the spin states as a synthetic spatial dimension, we show two particles are enough to simulate well known topological properties in condensed matter physics.

quant-ph↗

arXiv2022

Synthetic gauge field in two interacting ultracold atomic gases without an optical lattice

A 2D Fock-state lattice (FSL is constructed from the many-body states of two interacting two-mode quantum gases. By periodically driving the interspecies interactions and pulsing the tunneling between the two modes of each gas, a synthetic gauge field is generated. We derive an effective Hamiltonian in the short pulse limit which resembles the Harper-Hofstadter Hamiltonian where the magnetic flux per plaquette is controlled by the ratio of the interaction energy and the driving frequency. The quasispectrum of the Floquet operator of the driving sequence shows the celebrated Hofstadter's butterfly pattern as well as the existence of edge states. From the calculation of the local Chern marker, we establish that the FSL has non-trivial topology and by simulating the dynamics of the edge states, show that they exhibit chirality. Finally, the inclusion of the intraspecies interactions creates an overall harmonic trap in the lattice and introduces the nonlinear effect of macroscopic quantum self-trapping which is shown to hinder the movement along the edge of the lattice. This work introduces a new avenue to explore synthetic gauge fields and provides a link between non-trivial condensed matter systems and quantum gases.

cond-mat.quant-gas↗

arXiv2022

Meissner effect in Fock space

By periodically driving a single bosonic Josephson junction (BJJ) with an impurity, a synthetic gauge field is generated in the Fock space of the system. At a critical synthetic gauge flux the ground state undergoes a quantum phase transition which is analogous to the Meissner-Abrikosov-vortex transition found in type-II superconductors with an applied magnetic field. A second quantum phase transition involving attractive interactions between the bosons of the BJJ is shown to enhance the sensitivity of the system to the Meissner-Abrikosov-vortex transition.

quant-ph↗

arXiv2021

False signals of chaos from quantum probes

We demonstrate that two-time correlation functions, which are generalizations of out-of-time-ordered correlators (OTOCs), can show 'false-flags' of chaos by exhibiting behaviour predicted by random matrix theory even in a system with classically regular dynamics. In particular, we analyze a system of bosons trapped in a double-well potential and probed by a quantum dot which is coupled to the bosons dispersively. This is an integrable system (considered both as separate parts and in total). Despite the continuous time evolution generated by the actual Hamiltonian, we find that the n-fold two-time correlation function for the probe describes an effective stroboscopic or Floquet dynamics whereby the bosons appear to be alternately driven by two different non-commuting Hamiltonians in a manner reminiscent of the Trotterized time evolution that occurs in digital quantum simulation. The classical limit of this effective dynamics can have a nonzero Lyapunov exponent, while the effective level statistics and return probability show traditional signatures of chaotic behaviour. In line with several other recent studies, this work highlights the fact that the behavior of OTOCs and their generalizations must be interpreted with some care.

quant-ph↗

arXiv2019

Emergence of singularities from decoherence: Quantum catastrophes

We use a master equation to study the dynamics of two coupled macroscopic quantum systems (e.g.\ a Josephson junction made of two Bose-Einstein condensates or two spin states of an ensemble of trapped ions) subject to a weak continuous measurement. If the coupling between the two systems is suddenly switched on the resulting dynamics leads to caustics (fold and cusp catastrophes) in the number-difference probability distribution, and at the same time the measurement gradually induces a quantum-to-classical transition. Decoherence is often invoked to help resolve paradoxes associated with macroscopic quantum mechanics, but here, on the contrary, caustics are well-behaved in the quantum (many-particle) theory and divergent in the classical (mean-field) theory. Caustics thus represent a breakdown of the classical theory towards which decoherence seems to inevitably lead. We find that measurement backaction plays a crucial role in softening the resulting singularities and calculate the modification to the Arnol'd index which governs the scaling of the caustic's amplitude with the number of atoms. The Arnol'd index acts as a critical exponent for the formation of singularities during quantum dynamics and its modification by the open nature of the system is analogous to the modification of the critical exponents of phase transitions occurring in open systems.

cond-mat.quant-gas↗

arXiv2019

Measuring out-of-time-ordered correlation functions with a single impurity qubit in a bosonic Josephson junction

We calculate the out-of-time-ordered correlation function (OTOC) of a single impurity qubit coupled to fully a connected many-particle system such as a bosonic Josephson junction or spins with long-range interactions. In these systems the qubit OTOC can be used to detect both ground state and excited state quantum phase transitions (QPTs), making it a robust order parameter that is considerably more sensitive than the standard one-body correlation function. Finite size scaling exponents for an $N$ body system can also be accurately extracted from the long-time OTOC dynamics, however, for short times there is a discrepancy due to the fact that the qubit has not had enough time to couple to the larger system. Our results show that the OTOC of even the smallest probe is enough to diagnose a QPT in fully connected models but, like a continuous measurement, can still cause a backaction effect which leads to weakly chaotic dynamics and gradual information scrambling.

quant-ph↗

arXiv2019

Quantum caustics and the hierarchy of light cones in quenched spin chains

We show that the light cone-like structures that form in spin chains after a quench are quantum caustics. Their natural description is in terms of catastrophe theory and this implies: 1) a hierarchy of light cone structures corresponding to the different catastrophes; 2) dressing by characteristic wave functions that obey scaling laws determined by the Arnol'd and Berry indices; 3) a network of vortex-antivortex pairs in space-time inside the cone. We illustrate the theory by giving explicit calculations for the transverse field Ising model and the XY model, finding fold catastrophes dressed by Airy functions and cusp catastrophes dressed by Pearcey functions; multisite correlation functions are described by higher catastrophes such as the hyperbolic umbilic. Furthermore, we find that the vortex pairs created inside the cone are sensitive to phase transitions in these spin models with their rate of production being determined by the dynamical critical exponent. More broadly, this work illustrates how catastrophe theory can be applied to singularities in quantum fields.

cond-mat.quant-gas↗

arXiv2019

Quantum spin dynamics in Fock space following quenches: Caustics and vortices

Caustics occur widely in dynamics and take on shapes classified by catastrophe theory. At finite wavelengths they produce interference patterns containing networks of vortices (phase singularities). Here we investigate caustics in quantized fields, focusing on the collective dynamics of quantum spins. We show that, following a quench, caustics are generated in the Fock space amplitudes specifying the many-body configuration and which are accessible in experiments with cold atoms, ions or photons. The granularity of quantum fields removes all singularities, including phase singularities, converting point vortices into nonlocal vortices that annihilate in pairs as the quantization scale is increased. Furthermore, the continuous scaling laws of wave catastrophes are replaced by discrete versions. Such `quantum catastrophes' are expected to be universal dynamical features of quantized fields.

cond-mat.quant-gas↗

arXiv2014

Critical exponents for an impurity in a bosonic Josephson junction: Position measurement as a phase transition

We use fidelity susceptibility to calculate quantum critical scaling exponents for a system consisting of $N$ identical bosons interacting with a single impurity atom in a double well potential (bosonic Josephson junction). Above a critical value of the boson-impurity interaction energy there is a spontaneous breaking of $\mathbb{Z}_2$ symmetry corresponding to a second order quantum phase transition from a balanced to an imbalanced number of particles in either the left or right hand well. We show that the exponents match those in the Lipkin-Meshkov-Glick and Dicke models suggesting that the impurity model is in the same universality class. The phase transition can be interpreted as a measurement of the position of the impurity by the bosons.

cond-mat.quant-gas↗

arXiv2011

Impurity in a Bose-Einstein condensate in a double well

We compare and contrast the mean-field and many-body properties of a Bose-Einstein condensate trapped in a double well potential with a single impurity atom. The mean-field solutions display a rich structure of bifurcations as parameters such as the boson-impurity interaction strength and the tilt between the two wells are varied. In particular, we study a pitchfork bifurcation in the lowest mean-field stationary solution which occurs when the boson-impurity interaction exceeds a critical magnitude. This bifurcation, which is present for both repulsive and attractive boson-impurity interactions, corresponds to the spontaneous formation of an imbalance in the number of particles between the two wells. If the boson-impurity interaction is large, the bifurcation is associated with the onset of a Schroedinger cat state in the many-body ground state. We calculate the coherence and number fluctuations between the two wells, and also the entanglement entropy between the bosons and the impurity. We find that the coherence can be greatly enhanced at the bifurcation.

cond-mat.quant-gas↗