arXiv subjects

N. R. Cooper

Publications and source records attributed to N. R. Cooper.

At least 19 recordsLinked to original sources

arXiv2026

Phase-space microscopes for quantum gases: Imaging conjugate variables and momentum-weighted densities

Quantum gas microscopes offer unprecedented insights into quantum many-body states of cold atomic gases. Here we introduce concrete protocols for extending quantum gas microscopes to measure in phase space, by mapping momentum onto auxiliary degrees of freedom and using positive operator-valued measures. We distinguish between two distinct operational modes. In the Husimi-Q phase space microscope, position and momentum are jointly measured; in this mode the fundamental quantum noise is distributed between position and momentum. Conversely, the averaged-mode phase space microscope extracts the spatial dependence of averages of the momentum density (and its moments); these averages can be retrieved with arbitrary spatial resolution. We illustrate the utility of these techniques in diverse physical settings.

cond-mat.quant-gas↗

arXiv2023

Topological Phase Transitions in the Disordered Haldane Model

We investigate the phases and phase transitions of the disordered Haldane model in the presence of on-site disorder. We use the real-space Chern marker and transfer matrices to extract critical exponents over a broad range of parameters. The disorder-driven transitions are consistent with the plateau transitions in the Integer Quantum Hall Effect (IQHE), in conformity with recent simulations of disordered Dirac fermions. Our numerical findings are compatible with an additional line of mass-driven transitions with a continuously varying correlation length exponent. The values interpolate between free Dirac fermions and the IQHE with increasing disorder strength. We also show that the fluctuations of the Chern marker exhibit a power-law divergence in the vicinity of both sets of transitions, yielding another varying exponent. We discuss the interpretation of these results.

cond-mat.str-el↗

arXiv2023

Quantum Oscillations in an Impurity-Band Anderson Insulator

We show that for a system of localized electrons in an impurity band, which form an Anderson insulating state at zero temperature, there can appear quantum oscillations of the magnetization, i.e. the Anderson insulator can exhibit the de Haas-van Alphen effect. This is possible when the electronic band from which the localized states are formed has an extremum that traces out a nonzero area in reciprocal space. Our work extends existing theories for clean band insulators of this form to the situation where they host an impurity band. We show that the energies of these impurity levels oscillate with magnetic field, and compute the conditions under which these oscillations can dominate the de Haas-van Alphen effect. We discuss our results in connection with experimental measurements of quantum oscillations in Kondo insulators, and propose other experimental systems where the impurity band contribution can be dominant.

cond-mat.mes-hall↗

arXiv2022

Optical non-linearities and spontaneous translational symmetry breaking in driven-dissipative moiré exciton-polaritons

Moiré lattices formed from semiconductor bilayers host tightly localised excitons that can simultaneously couple strongly to light and possess large electric dipole moments. This facilitates the realization of new forms of polaritons that are very strongly interacting and that have been predicted to lead to strong optical nonlinearities controlled by multi-photon resonances. Here, we investigate the role of the non-local component of the exciton-exciton (dipolar) interactions on the optical response of these strongly-interacting moiré exciton-polaritons under conditions of strong optical driving. We find that the non-local interactions can strongly influence the steady-state properties leading to multi-stabilities with broken translational symmetry and pronounced distortions of the multi-photon resonances. We develop a self-consistent approach to describe the steady-state solution of moiré excitons coupled to a cavity field, treating the long-range interaction between the excitons and the photon field at the semi-classical level.

cond-mat.mes-hall↗

arXiv2019

P-band induced self-organization and dynamics with repulsively driven ultracold atoms in an optical cavity

We investigate a Bose-Einstein condensate strongly coupled to an optical cavity via a repulsive optical lattice. We detect a stable self-ordered phase in this regime, and show that the atoms order through an antisymmetric coupling to the P-band of the lattice, limiting the extent of the phase and changing the geometry of the emergent density modulation. Furthermore, we find a non-equilibrium phase with repeated intense bursts of the intra-cavity photon number, indicating non-trivial driven-dissipative dynamics.

cond-mat.quant-gas↗

arXiv2019

Steady states of a driven dissipative dipolar XXZ chain

We study theoretically a driven dissipative one-dimensional XXZ spin$-1/2$ chain with dipole coupling and a tunable strength of the Ising and XY interaction. Within a mean-field approximation, we find a rich phase diagram with uniform, spin density wave, antiferromagnetic and oscillatory phases, as well as regions of phase bistability. We study the phase diagram of small quantum systems using exact diagonalisation, and compare the results to the mean-field theory. We find that while expectation values only capture the uniform phases of the mean-field theory, fluctuations about these expectation values give signatures of spatially non-uniform phases and bistabilities. We find these signatures for all ratios of the Ising to XY interaction, showing that they appear to be general features of spin$-1/2$ systems

cond-mat.quant-gas↗

arXiv2018

Decay rates and energies of free magnons and bound states in dissipative XXZ chains

Chains of coupled two-level atoms behave as 1D quantum spin systems, exhibiting free magnons and magnon bound states. While these excitations are well studied for closed systems, little consideration has been given to how they are altered by the presence of an environment. This will be especially important in systems that exhibit nonlocal dissipation, e.g. systems in which the magnons decay due to optical emission. In this work, we consider free magnon excitations and two-magnon bound states in an XXZ chain with nonlocal dissipation. We prove that whilst the energy of the bound state can lie outside the two-magnon continuum of energies, the decay rate of the bound state has to always lie within the two-magnon continuum of decay rates. We then derive analytically the bound state solutions for a system with nearest-neighbour and next-nearest-neighbour XY interaction and nonlocal dissipation, finding that the inclusion of nonlocal dissipation allows more freedom in engineering the energy and decay rate dispersions for the bound states. Finally, we numerically study a model of an experimental set-up that should allow the realisation of dissipative bound states by using Rydberg-dressed atoms coupled to a photonic crystal waveguide (PCW). We demonstrate that this model can exhibit many key features of our simpler models.

cond-mat.quant-gas↗

arXiv2018

Topological Bands for Ultracold Atoms

There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. We describe the different methods that have been used to generate these novel bandstructures for cold atoms, as well as the physical observables that have allowed their characterization. We focus on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. However, we also describe how specific experimental implementations can influence physical properties. Moving beyond single-particle effects, we describe the forms of inter-particle interactions that emerge when atoms are subjected to these energy bands, and some of the many-body phases that may be sought in future experiments.

cond-mat.quant-gas↗

arXiv2018

Topological Marker Currents in Chern Insulators

Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However, local topological markers can distinguish between topological phases, and they can vary in space. In equilibrium, we show that the topological marker can be used to extract the critical behavior of topological phase transitions. Out of equilibrium, we show that the topological marker spreads via a flow of currents, with a bounded maximum propagation speed. We discuss the possibilities for measuring the topological marker and its flow in experiment.

cond-mat.str-el↗

arXiv2018

Phases of driven two-level systems with nonlocal dissipation

We study an array of two-level systems arranged on a lattice and illuminated by an external plane wave which drives a dipolar transition between the two energy levels. In this set up, the two-level systems are coupled by dipolar interactions and subject to nonlocal dissipation, so behave as an open many-body quantum system. We investigate the long-time dynamics of the system at the mean-field level, and use this to determine a phase diagram as a function of external drive and detuning. We find a multitude of phases including antiferromagnetism, spin density waves, oscillations and phase bistabilities. We investigate these phases in more detail and explain how nonlocal dissipation plays a role in the long-time dynamics. Furthermore, we discuss what features would survive in the full quantum description.

cond-mat.quant-gas↗

arXiv2017

A Spectroscopic Method to Measure the Superfluid Fraction of an Ultracold Atomic Gas

We perform detailed analytical and numerical studies of a recently proposed method for a spectroscopic measurement of the superfluid fraction of an ultracold atomic gas [N. R. Cooper and Z. Hadzibabic, Phys. Rev. Lett. 104, 030401 (2010)]. Previous theoretical work is extended by explicitly including the effects of non-zero temperature and interactions, and assessing the quantitative accuracy of the proposed measurement for a one-component Bose gas. We show that for suitably chosen experimental parameters the method yields an experimentally detectable signal and a sufficiently accurate measurement. This is illustrated by explicitly considering two key examples: First, for a weakly interacting three-dimensional Bose gas it reproduces the expected result that below the critical temperature the superfluid fraction closely follows the condensate fraction. Second, it allows a clear quantitative differentiation of the superfluid and the condensate density in a strongly interacting Bose gas.

cond-mat.quant-gas↗

arXiv2017

Synchronization transition in dipole-coupled two-level systems with positional disorder

We study the decoherence dynamics of dipole-coupled two-level quantum systems in Ramsey-type experiments. We focus on large networks of two-level systems, confined to two spatial dimensions and with positional disorder giving rise to disordered dipolar couplings. This setting is relevant for modeling the decoherence dynamics of the rotational excitations of polar molecules confined to deep optical lattices, where disorder arises from the random filling of lattice sites with occupation probability $p$. We show that the decoherence dynamics exhibits a phase transition at a critical filling $p_c\simeq 0.15$. For $p p_c$ the dipolar interactions dominate the disorder, and the system behaves as a collective spin-ordered phase, representing synchronization of the two-level systems and persistent Ramsey oscillations with divergent $T_2$ for large systems. For a finite number of two-level systems, $N$, the spin-ordered phase at $p> p_c$ undergoes a crossover to a collective spin-squeezed state on a timescale $τ_{\rm sq} \propto \sqrt{N}$. We develop a self-consistent mean-field theory that is capable of capturing the synchronization transition at $p_c$, and provide an intuitive theoretical picture that describes the phase transition in the long-time dynamics. We also show that the decoherence dynamics appear to be ergodic in the vicinity of $p_c$, the long-time behaviour being well described by the predictions of equilibrium thermodynamics. The results are supported by the results of exact diagonalization studies of small systems.

cond-mat.quant-gas↗

arXiv2017

Stable Collective Dynamics of Two-Level Systems Coupled by Dipole Interactions

We study the dynamics of a set of two-level systems coupled by dipolar interactions under a resonant external Rabi drive. The two-level systems are prepared initially in a coherent product state, and we ask how the non-equilibrium conditions caused by the drive affect this coherence. We study the full non-linear dynamics of the coupled two-level systems within a classical approximation by analysing numerically the equations of motion and determining the stability of the collective coherent state within classical Floquet theory. We establish the behaviour analytically in the high Rabi coupling limit by employing a Magnus expansion and spin wave analysis. Our results show that, typically, the dipole interactions between the two-level systems lead to instabilities that cause a breakdown of the collective Rabi oscillations. However, we identify parameter regimes for which the two-level systems undergo collective coherent Rabi oscillations even in the presence of the dipole interactions.

cond-mat.quant-gas↗

arXiv2016

Hall Response and Edge Current Dynamics in Chern Insulators out of Equilibrium

We investigate the transport properties of Chern insulators following a quantum quench between topological and non-topological phases. Recent works have shown that this yields an excited state for which the Chern number is preserved under unitary evolution. However, this does not imply the preservation of other physical observables, as we stressed in our previous work. Here we provide an analysis of the Hall response following a quantum quench in an isolated system, with explicit results for the Haldane model. We show that the Hall conductance is no longer related to the Chern number in the post-quench state, in agreement with previous work. We also examine the dynamics of the edge currents in finite-size systems with open boundary conditions along one direction. We show that the late-time behavior is captured by a Generalized Gibbs Ensemble, after multiple traversals of the sample. We discuss the effects of generic open boundary conditions and confinement potentials.

cond-mat.str-el↗

arXiv2015

Quantum Quenches in Chern Insulators

We explore the non-equilibrium response of Chern insulators. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and non-topological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench. However, in finite geometries, the initial and final Hamiltonians are distinguished by the presence or absence of edge modes. We study the edge excitations and describe their impact on the experimentally-observable edge currents and magnetization. We show that, following a quantum quench, the edge currents relax towards new equilibrium values, and that there is light-cone spreading of the currents into the interior of the sample.

cond-mat.str-el↗

arXiv2015

Adiabatic Control of Atomic Dressed States for Transport and Sensing

We describe forms of adiabatic transport that arise for dressed-state atoms in optical lattices. Focussing on the limit of weak tunnel-coupling between nearest-neighbour lattice sites, we explain how adiabatic variation of optical dressing allows control of atomic motion between lattice sites: allowing adiabatic particle transport in a direction that depends on the internal state, and force measurements via spectroscopic preparation and readout. For uniformly filled bands these systems display topologically quantised particle transport.

cond-mat.quant-gas↗

arXiv2015

Periodically-driven quantum matter: the case of resonant modulations

Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a time-independent effective Hamiltonian, which is generally identified through a perturbative treatment. Here, we present a general formalism that describes time-modulated physical systems, in which the driving frequency is large, but resonant with respect to energy spacings inherent to the system at rest. Such a situation is currently exploited in optical-lattice setups, where superlattice (or Wannier-Stark-ladder) potentials are resonantly modulated so as to control the tunneling matrix elements between lattice sites, offering a powerful method to generate artificial fluxes for cold-atom systems. The formalism developed in this work identifies the basic ingredients needed to generate interesting flux patterns and band structures using resonant modulations. Additionally, our approach allows for a simple description of the micro-motion underlying the dynamics; we illustrate its characteristics based on diverse dynamic-lattice configurations. It is shown that the impact of the micro-motion on physical observables strongly depends on the implemented scheme, suggesting that a theoretical description in terms of the effective Hamiltonian alone is generally not sufficient to capture the full time-evolution of the system.

cond-mat.quant-gas↗

arXiv2014

Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms

Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic metals. A striking manifestation of this transverse transport was then revealed in the quantum Hall effect, where the plateaus depicted by the Hall conductivity were attributed to a topological invariant characterizing Bloch bands: the Chern number. Until now, topological transport associated with non-zero Chern numbers has only been revealed in electronic systems. Here we use studies of an atomic cloud's transverse deflection in response to an optical gradient to measure the Chern number of artificially generated Hofstadter bands. These topological bands are very flat and thus constitute good candidates for the realization of fractional Chern insulators. Combining these deflection measurements with the determination of the band populations, we obtain an experimental value for the Chern number of the lowest band $ν_{\mathrm{exp}} =0.99(5)$. This result, which constitutes the first Chern-number measurement in a non-electronic system, is facilitated by an all-optical artificial gauge field scheme, generating uniform flux in optical superlattices.

cond-mat.quant-gas↗