44 results found
Sykes J, Barnett R, 2022, 1D quasicrystals and topological markers, Materials for Quantum Technology, Vol: 2, Pages: 025005-025005, ISSN: 2633-4356
Local topological markers are effective tools for determining the topological properties of bothhomogeneous and inhomogeneous systems. The Chern marker is an established topologicalmarker that has previously been shown to effectively reveal the topological properties of 2Dsystems. In an earlier work, the present authors have developed a marker that can be applied to 1Dtime-dependent systems which can be used to explore their topological properties, like chargepumping under the presence of disorder. In this paper, we show how to alter the 1D marker so thatit can be applied to quasiperiodic and aperiodic systems. We then verify its effectiveness againstdifferent quasicrystal Hamiltonians, some which have been addressed in previous studies usingexisting methods, and others which possess topological structures that have been largelyunexplored. We also demonstrate that the altered 1D marker can be productively applied tosystems that are fully aperiodic.
Barnett R, Jager J, 2021, A stochastic fields approach to the quench dynamics of a one dimensional Bose polaron, Physical Review Research, Vol: 3, Pages: 1-10, ISSN: 2643-1564
We consider the dynamics of a quantum impurity after a sudden interaction quench into a onedimensional degenerate Bose gas. We use the Keldysh path integral formalism to derive a truncatedWigner like approach that takes the back action of the impurity onto the condensate into accountalready on the mean-field level and further incorporates thermal and quantum effects up to oneloop accuracy. This framework enables us not only to calculate the real space trajectory of theimpurity but also the absorption spectrum. We find that quantum corrections and thermal effectsplay a crucial role for the impurity momentum at weak to intermediate impurity-bath couplings.Furthermore, we see the broadening of the absorption spectrum with increasing temperature.
Sykes J, Barnett R, 2021, Local Topological Markers in Odd Dimensions, Phys. Rev. B, Vol: 103
Local topological markers have proven to be a valuable tool for investigatingsystems with topologically non-trivial bands. Due to their local nature, suchmarkers can treat translationally invariant systems and spatially inhomogeneoussystems on an equal footing. Among the most prevalent of these is the so-calledChern marker, which is available for systems in two spatial dimensions. In thispaper, we describe how to generalize this marker to 1d and 3d systems, byshowing that the relevant expressions accurately describe the phenomenon oftopological pumping given by the first and second Chern numbers in 1d and 3drespectively. In addition to providing general derivations, we verify themarkers by numerically considering model Hamiltonians. These results will openthe door for future studies including the influence of disorder on topologicalpumping and topological phase transitions in odd-dimensional systems.
Jager J, Barnett R, Will M, et al., 2020, Strong-coupling Bose polarons in one dimension: Condensate deformation and modified Bogoliubov phonons, Physical Review Research, Vol: 2, Pages: 033142 – 1-033142 – 8, ISSN: 2643-1564
We discuss the interaction of a quantum impurity with a one-dimensional degenerate Bose gas forming a Bose polaron. In three spatial dimension, the quasiparticle is typically well described by the extended Fröhlich model, in full analogy with the solid-state counterpart. This description, which assumes an undepleted condensate, fails, however, in 1D, where the backaction of the impurity on the condensate leads to a self-bound mean-field polaron for arbitrarily weak impurity-boson interactions. We present a model that takes into account this backaction and describes the impurity-condensate interaction as coupling to phononlike excitations of a deformed condensate. A comparison of polaron energies and masses to diffusion quantum Monte Carlo simulations shows very good agreement already on the level of analytical mean-field solutions and is further improved when taking into account quantum fluctuations.
Mingarelli L, Barnett R, 2019, Exotic vortex lattices in binary repulsive superfluids, Physical Review Letters, Vol: 122, ISSN: 0031-9007
We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: m1≠m2. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich vortex lattice configurations, a number of which correspond to Platonic and Archimedean planar tilings. Some notable geometries include the snub-square, honeycomb, kagome, and herringbone lattice configurations. We present a full phase diagram for the case m2/m1=2 and list a number of geometries that are found for higher integer mass ratios.
Wrubel JP, Schwettmann A, Fahey DP, et al., 2018, Spinor Bose-Einstein-condensate phase-sensitive amplifier for SU(1,1) interferometry, Physical Review A, Vol: 98, ISSN: 2469-9926
The SU(1,1) interferometer was originally conceived as a Mach-Zehnder interferometer with the beam splitters replaced by parametric amplifiers. The parametric amplifiers produce states with correlations that result in enhanced phase sensitivity. F=1 spinor Bose-Einstein condensates (BECs) can serve as the parametric amplifiers for an atomic version of such an interferometer by collisionally producing entangled pairs of |F=1,m=±1) atoms. We simulate the effect of single- and double-sided seeding of the inputs to the amplifier using the truncated-Wigner approximation. We find that single-sided seeding degrades the performance of the interferometer exactly at the phase the unseeded interferometer should operate the best. Double-sided seeding results in a phase-sensitive amplifier, where the maximal sensitivity is a function of the phase relationship between the input states of the amplifier. In both single- and double-sided seeding we find there exists an optimal phase shift that achieves sensitivity beyond the standard quantum limit. Experimentally, we demonstrate a spinor phase-sensitive amplifier using a BEC of Na23 in an optical dipole trap. This configuration could be used as an input to such an interferometer. We are able to control the initial phase of the double-seeded amplifier and demonstrate sensitivity to initial population fractions as small as 0.1%.
Mingarelli L, Keaveny EE, Barnett R, 2018, Vortex lattices in binary mixtures of repulsive superfluids, Physical Review A, Vol: 97, ISSN: 1050-2947
We present an extension of the framework introduced in previous work [L. Mingarelli, E. E. Keaveny, and R. Barnett, J. Phys.: Condens. Matter 28, 285201 (2016)JCOMEL0953-898410.1088/0953-8984/28/28/285201] to treat multicomponent systems, showing that new degrees of freedom are necessary in order to obtain the desired boundary conditions. We then apply this extended framework to the coupled Gross-Pitaevskii equations to investigate the ground states of two-component systems with equal masses, thereby extending previous work in the lowest Landau limit [E. J. Mueller and T.-L. Ho, Phys. Rev. Lett. 88, 180403 (2002)PRLTAO0031-900710.1103/PhysRevLett.88.180403] to arbitrary interactions within Gross-Pitaevskii theory. We show that away from the lowest Landau level limit, the predominant vortex lattice consists of two interlaced triangular lattices. Finally, we derive a linear relation which accurately describes the phase boundaries in the strong interacting regimes.
Galilo B, Lee DKK, Barnett R, 2017, Topological edge state manifestation of interacting 2D boson lattices in a harmonic trap, Physical Review Letters, Vol: 119, ISSN: 0031-9007
In this Letter, it is shown that interactions can facilitate the emergence of topological edge states of quantum-degenerate bosonic systems in the presence of a harmonic potential. This effect is demonstrated with the concrete model of a hexagonal lattice populated by spin-one bosons under a synthetic gauge field. In fermionic or noninteracting systems, the presence of a harmonic trap can obscure the observation of edge states. For our system with weakly interacting bosons in the Thomas-Fermi regime, we can clearly see a topological band structure with a band gap traversed by edge states. We also find that the number of edge states crossing the gap is increased in the presence of a harmonic trap, and the edge modes experience an energy shift while traversing the first Brillouin zone which is related to the topological properties of the system. We find an analytical expression for the edge-state energies and our comparison with numerical computation shows excellent agreement.
Jevtic S, Barnett R, 2017, Frustration-free Hamiltonians supporting Majorana zero edge modes, New Journal of Physics, Vol: 19, ISSN: 1367-2630
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.
Barnett RL, Payrits M, 2016, Quantum Rotor Theory of Systems of Spin-2 Bosons, Physical Review A, Vol: 94, ISSN: 1094-1622
We consider quantum phases of tightly-confined spin-2 bosons in an external field under thepresence of rotationally-invariant interactions. Generalizing previous treatments, we show how thissystem can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitationsabout fragmented states, which cannot be accessed within standard Bogoliubov theory, canbe obtained. In the spatially extended system in the thermodynamic limit there exists a mean-fieldground state degeneracy between a family of nematic states for appropriate interaction parameters.It has been established that quantum fluctuations lift this degeneracy through the mechanism oforder-by-disorder and select either a uniaxial or square-biaxial ground state. On the other hand, inthe full quantum treatment of the analogous single-spatial mode problem with finite particle numberit is known that, due to symmetry restoring fluctuations, there is a unique ground state across theentire nematic region of the phase diagram. Within the established rotor framework we investigatethe possible quantum phases under the presence of a quadratic Zeeman field, a problem which haspreviously received little attention. By investigating wave function overlaps we do not find anysignatures of the order-by-disorder phenomenon which is present in the continuum case. Motivatedby this we consider an alternative external potential which breaks less symmetry than the quadraticZeeman field. For this case we do find the phenomenon of order-by-disorder in the fully quantumsystem. This is established within the rotor framework and with exact diagonalization.
Mingarelli L, Keaveny EE, Barnett R, 2016, Simulating infinite vortex lattices in superfluids, Journal of Physics: Condensed Matter, Vol: 28, ISSN: 0953-8984
We present an efficient framework to numerically treat infinite periodic vortex lattices in rotating superfluids described by the Gross–Pitaevskii theory. The commonly used split-step Fourier (SSF) spectral methods are inapplicable to such systems as the standard Fourier transform does not respect the boundary conditions mandated by the magnetic translation group. We present a generalisation of the SSF method which incorporates the correct boundary conditions by employing the so-called magnetic Fourier transform. We test the method and show that it reduces to known results in the lowest-Landau-level regime. While we focus on rotating scalar superfluids for simplicity, the framework can be naturally extended to treat multicomponent systems and systems under more general 'synthetic' gauge fields.
Barnett RL, Lee DKK, Galilo B, 2015, Selective population of edge states in a 2D topological band system, Physical Review Letters, Vol: 115, ISSN: 1079-7114
We consider a system of interacting spin-one atoms in a hexagonal lattice under the presence of a synthetic gauge field. Quenching the quadratic Zeeman field is shown to lead to a dynamical instability of the edge modes. This, in turn, leads to a spin current along the boundary of the system which grows exponentially fast in time following the quench. Tuning the magnitude of the quench can be used to selectively populate edge modes of different momenta. Implications of the intrinsic symmetries of the Hamiltonian on the dynamics are discussed. The results hold for atoms with both antiferromagnetic and ferromagnetic interactions.
Payrits M, Barnett R, 2014, Order-by-disorder degeneracy lifting of interacting bosons on the dice lattice, Physical Review A, Vol: 90, ISSN: 1094-1622
Motivated by recent experimental progress in the realization of synthetic gauge fields in systems of ultracold atoms, we consider interacting bosons on the dice lattice with half flux per plaquette. All bands of thenoninteracting spectrum of this system were previously found to have the remarkable property of being completely dispersionless. We show that degeneracies remain when interactions are treated at the level of mean-field theory, and the ground state exhibits vortex lattice configurations already established in the simpler XY model in thesame geometry. We argue that including quantum and thermal fluctuations will select a unique vortex lattice up to overall symmetries based on the order-by-disorder mechanism. We verify the stability of the selected state by analyzing the condensate depletion. The latter is shown to exhibit an unusual nonmonotonic behavior as afunction of the interaction parameters which can be understood as a consequence of the dispersionless nature of the noninteracting spectrum. Finally, we comment on the role of domain walls which have interactions mediated through fluctuations.
Barnett R, 2013, Edge-state instabilities of bosons in a topological band, PHYSICAL REVIEW A, Vol: 88, ISSN: 1050-2947
Pechkis HK, Wrubel JP, Schwettmann A, et al., 2013, Spinor Dynamics in an Antiferromagnetic Spin-1 Thermal Bose Gas, Phys. Rev. Lett., Vol: 111, Pages: 025301-025301
Hui H-Y, Barnett R, Porto JV, et al., 2012, Loop-structure stability of a double-well-lattice Bose-Einstein condensate, PHYSICAL REVIEW A, Vol: 86, ISSN: 1050-2947
Barnett R, Powell S, Grass T, et al., 2012, Order by disorder in spin-orbit-coupled Bose-Einstein condensates (vol 85, 023615, 2012), PHYSICAL REVIEW A, Vol: 85, ISSN: 1050-2947
Barnett R, Boyd GR, Galitski V, 2012, SU (3) Spin-Orbit Coupling in Ultracold Atoms, Arxiv preprint arXiv:1207.1728
Barnett R, Powell S, Grass T, et al., 2012, Order by disorder in spin-orbit coupled Bose-Einstein Condensates, Physical Review A, Vol: 85
Barnett R, Polkovnikov A, Vengalattore M, 2011, Prethermalization in quenched spinor condensates, Physical Review A, Vol: 84, Pages: 023606-023606
Barnett R, Hui HY, Lin CH, et al., 2011, Quantum rotor theory of spinor condensates in tight traps, Physical Review A, Vol: 83, ISSN: 1050-2947
In this work, we theoretically construct exact mappings of many-particle bosonic systems onto quantum rotor models. In particular, we analyze the rotor representation of spinor Bose-Einstein condensates. In a previous work [R. Barnett et al., Phys. Rev. A 82, 031602(R) (2010)] it was shown that there is an exact mapping of a spin-one condensate of fixed particle number with quadratic Zeeman interaction onto a quantum rotor model. Since the rotor model has an unbounded spectrum from above, it has many more eigenstates than the original bosonic model. Here we show that for each subset of states with fixed spin Fz, the physical rotor eigenstates are always those with the lowest energy. We classify three distinct physical limits of the rotor model: the Rabi, Josephson, and Fock regimes. The last regime corresponds to a fragmented condensate and is thus not captured by the Bogoliubov theory. We next consider the semiclassical limit of the rotor problem and make connections with the quantum wave functions through the use of the Husimi distribution function. Finally, we describe how to extend the analysis to higher-spin systems and derive a rotor model for the spin-two condensate. Theoretical details of the rotor mapping are also provided here.
Powell S, Barnett R, Sensarma R, et al., 2011, Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field, Physical Review A, Vol: 83, Pages: 013612-013612
Hui HY, Barnett R, Sensarma R, et al., 2011, Instabilities of bosonic spin currents in optical lattices, Physical Review A, Vol: 84, Pages: 043615-043615
Barnett R, Chen E, Refael G, 2010, Vortex synchronization in Bose–Einstein condensates: a time-dependent Gross–Pitaevskii equation approach, New Journal of Physics, Vol: 12, Pages: 043004-043004
Powell S, Barnett R, Sensarma R, et al., 2010, Interacting Hofstadter spectrum of atoms in an artificial gauge field, Physical Review Letters, Vol: 104, Pages: 255303-255303
Zou Y, Barnett R, Refael G, 2010, Particle-hole symmetric localization in optical lattices using time modulated random on-site potentials, Physical Review B, Vol: 82, Pages: 224205-224205
Barnett R, Sau JD, Sarma SD, 2010, Antiferromagnetic spinor condensates are quantum rotors, Physical Review A, Vol: 82, Pages: 031602-031602
Barnett R, Podolsky D, Refael G, 2009, Geometrical approach to hydrodynamics and low-energy excitations of spinor condensates, Physical Review B, Vol: 80, Pages: 024420-024420
Barnett R, Refael G, Porter MA, et al., 2008, Vortex lattice locking in rotating two-component Bose-Einstein condensates, NEW JOURNAL OF PHYSICS, Vol: 10, ISSN: 1367-2630
Barnett R, Mukerjee S, Moore JE, 2008, Vortex lattice transitions in cyclic spinor condensates, Physical Review Letters, Vol: 100, Pages: 240405-240405
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