arXiv subjects

Patrik Ohberg

Publications and source records attributed to Patrik Ohberg.

17 recordsLinked to original sources

arXiv2017

Universality and tails of long range interactions in one dimension

Long-range interactions and, in particular, two-body potentials with power-law long-distance tails are ubiquitous in nature. For two bosons or fermions in one spatial dimension, the latter case being formally equivalent to three-dimensional $s$-wave scattering, we show how generic asymptotic interaction tails can be accounted for in the long-distance limit of scattering wave functions. This is made possible by introducing a generalisation of the collisional phase shifts to include space dependence. We show that this distance dependence is universal, in that it does not depend on short-distance details of the interaction. The energy dependence is also universal, and is fully determined by the asymptotic tails of the two-body potential. As an important application of our findings, we describe how to eliminate finite-size effects with long-range potentials in the calculation of scattering phase shifts from exact diagonalisation. We show that even with moderately small system sizes it is possible to accurately extract phase shifts that would otherwise be plagued with finite-size errors. We also consider multi-channel scattering, focusing on the estimation of open channel asymptotic interaction strengths via finite-size analysis.

cond-mat.quant-gas↗

arXiv2017

Driven Topological Systems in the Classical Limit

Periodically-driven quantum systems can exhibit topologically non-trivial behaviour, even when their quasi-energy bands have zero Chern numbers. Much work has been conducted on non-interacting quantum-mechanical models where this kind of behaviour is present. However, the inclusion of interactions in out-of-equilibrium quantum systems can prove to be quite challenging. On the other hand, the classical counterpart of hard-core interactions can be simulated efficiently via constrained random walks. The non-interacting model proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013)], has a special point for which the system is equivalent to a classical random walk. We consider the classical counterpart of this model, which is exact at a special point even when hard-core interactions are present, and show how these quantitatively affect the edge currents in a strip geometry. We find that the interacting classical system is well described by a mean-field theory. Using this we simulate the dynamics of the classical system, which show that the interactions play the role of Markovian, or time dependent disorder. By comparing the evolution of classical and quantum edge currents in small lattices, we find regimes where the classical limit considered gives good insight into the quantum problem.

cond-mat.other↗

arXiv2016

Few-Body Route to One-Dimensional Quantum Liquids

Gapless many-body quantum systems in one spatial dimension are universally described by the Luttinger liquid effective theory at low energies. Essentially, only two parameters enter the effective low-energy description, namely the speed of sound and the Luttinger parameter. These are highly system dependent and their calculation requires accurate non-perturbative solutions of the many-body problem. Here, we present a simple method that only uses collisional information to extract the low-energy properties of these systems. Our results are in remarkable agreement with available results for integrable models and from large scale Monte Carlo simulations of one-dimensional helium and hydrogen isotopes. Moreover, we estimate theoretically the critical point for spinodal decomposition in one-dimensional helium-4, and show that the exponent governing the divergence of the Luttinger parameter near the critical point is exactly 1/2, in excellent agreement with Monte Carlo simulations.

cond-mat.quant-gas↗

arXiv2015

Fermionic Luttinger liquids from a microscopic perspective

We consider interacting one-dimensional, spinless Fermi gases, whose low-energy properties are described by Luttinger liquid theory. We perform a systematic, in-depth analysis of the relation between the macroscopic, phenomenological parameters of Luttinger liquid effective field theory, and the microscopic interactions of the Fermi gas. In particular, we begin by explaining how to model effective interactions in one dimension, which we then apply to the main forward scattering channel -- the interbranch collisions -- common to these systems. We renormalise the corresponding interbranch phenomenological constants in favour of scattering phase shifts. Interestingly, our renormalisation procedure shows (i) how Luttinger's model arises in a completely natural way -- and not as a convenient approximation -- from Tomonaga's model, and (ii) the reasons behind the interbranch coupling constant remaining unrenormalised in Luttinger's model. We then consider the so-called intrabranch processes, whose phenomenological coupling constant is known to be fixed by charge conservation, but whose microscopic origin is not well understood. We show that, contrary to general belief and common sense, the intrabranch interactions appearing in Luttinger liquid theory do not correspond to an intrabranch scattering channel, nor an energy shift due to intrabranch interactions, in the microscopic theory. Instead, they are due to interbranch processes. We finally apply our results to a particular example of an exactly solvable model, namely the fermionic dual to the Lieb-Liniger model in the Tonks-Girardeau and super-Tonks-Girardeau regimes.

cond-mat.quant-gas↗

arXiv2014

Markovian evolution of strongly coupled harmonic oscillators

We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators which are subject to individual heat baths modeled by a collection of harmonic oscillators, and show that this master equation in general contains non-local Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator, and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled, and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.

quant-ph↗

arXiv2014

The Raman dressed spin-1 spin-orbit coupled quantum gas

The recently realized spin-orbit coupled quantum gases (Y.-J Lin {\it et al}., Nature 471, 83-86 (2011); P. Wang {\it et al}., PRL 109, 095301 (2012); L. W. Cheuk {\it et al}., PRL 109, 095302 (2012)) mark a breakthrough in the cold atom community. In these experiments, two hyperfine states are selected from a hyperfine manifold to mimic a pseudospin-1/2 spin-orbit coupled system by the method of Raman dressing, which is applicable to both bosonic and fermionic gases. In this work, we show that the method used in these experiments can be generalized to create any large pseudospin spin-orbit coupled gas if more hyperfine states are coupled equally by the Raman lasers. As an example, we study in detail a quantum gas with three hyperfine states coupled by the Raman lasers, and show when the state-dependent energy shifts of the three states are comparable, triple-degenerate minima will appear at the bottom of the band dispersions, thus realizing a spin-1 spin-orbit coupled quantum gas. A novel feature of this three minima regime is that there can be two different kinds of stripe phases with different wavelengths, which has an interesting connection to the ferromagnetic and polar phases of spin-1 spinor BECs without spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2013

Non-Galilean response of Rashba coupled Fermi gases

We consider the effect of a momentum kick on the ground state of a non-interacting two-dimensional Fermi gas subject to Rashba spin-orbit coupling. Although the total momentum is a constant of motion, the gas does not obey the rules of Galilean relativity. Upon imprinting a small overall velocity to the non-interacting gas, we find that the Fermi sea is deformed in a non-trivial way. We also consider a weakly repulsive Fermi gas, and find, from its Hartree shift, that the total ground state of the system may change into a deformed, finite momentum ground state as the repulsion is increased beyond a critical value, without the need of any external Zeeman fields. We also discuss possible experimental signatures of these effects.

cond-mat.quant-gas↗

arXiv2013

Simulating an interacting gauge theory with ultracold Bose gases

We show how density dependent gauge potentials can be induced in dilute gases of ultracold atoms using light-matter interactions. We study the effect of the resulting interacting gauge theory and show how it gives rise to novel topological states in the ultracold gas. We find in particular that the onset of persistent currents in a ring geometry is governed by a critical number of particles. The density-dependent gauge potential is also found to support chiral solitons in a quasi-one-dimensional ultracold Bose gas.

cond-mat.quant-gas↗

arXiv2013

Constructive role of dissipation for driven coupled bosonic modes

We theoretically investigate a system of two coupled bosonic modes subject to both dissipation and external driving. We show that in the steady state the degree of entanglement between the coupled bosonic modes can be enhanced by dissipation. The non-monotonic dependence of entanglement on the decay rates is observed when the bosonic modes are asymmetrically coupled to their local baths. This counterintuitive result opens a new way to better understand the interplay between noise and coherence in continuous variable systems driven away from equilibrium.

quant-ph↗

arXiv2013

On the Josephson effect in a Bose-Einstein condensate subject to a density dependent gauge potential

We investigate the coherent dynamics of a Bose-Einstein condensate in a double well, subject to a density dependent gauge potential. Further, we derive the nonlinear Josephson equations that allow us to understand the many-body system in terms of a classical Hamiltonian that describes the motion of a nonrigid pendulum with an initial angular offset. Finally we analyze the phase-space trajectories of the system, and describe how the self-trapping is affected by the presence of an interacting gauge potential.

cond-mat.quant-gas↗

arXiv2012

Single-branch theory of ultracold Fermi gases with artificial Rashba spin-orbit coupling

We consider interacting ultracold fermions subject to Rashba spin-orbit coupling. We construct a single-branch interacting theory for the Fermi gas when the system is dilute enough so that the positive helicity branch is not occupied at all in the non-interacting ground state. We show that the theory is renormalizable in perturbation theory and therefore yields a model of polarized fermions that avoids a multi-channel treatment of the problem. Our results open the path towards a much more straightforward approach to the many-body physics of cold atoms subject to artificial vector potentials.

cond-mat.quant-gas↗

arXiv2012

How general are time-local master equations?

Time-local master equations are more generally applicable than is often recognised, but at first sight it would seem that they can only safely be used in time intervals where the time evolution is invertible. Using the Jaynes-Cummings model, we here construct an explicit example where two different Hamiltonians, corresponding to two different non-invertible and non-Markovian time evolutions, will lead to arbitrarily similar time-local master equations. This illustrates how the time-local master equation on its own in this case does not uniquely determine the time evolution. The example is nevertheless artificial in the sense that a rapid change in (at least) one of the Hamiltonians is needed. The change must also occur at a very specific instance in time. If a Hamiltonian is known not to have such very specific behaviour, but is "physically well-behaved", then one may conjecture that a time-local master equation also determines the time evolution when it is not invertible.

quant-ph↗

arXiv2012

Coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice

We investigate the properties of an edge-centered honeycomb lattice, and show that this lattice features both spin-1/2 and spin-1 Dirac-Weyl fermions at different filling fractions f (f=1/5,4/5 for spin-1/2 and f=1/2 for spin-1). This five-band system is the simplest lattice that can support simultaneously the two different paradigmatic Dirac-Weyl fermions with half-integer spin and integer spin. We demonstrate that these pseudo-relativistic structures, including a flat band at half-filling, can be deduced from the underlying Kagome sublattice. We further show that the signatures of the two kinds of relativistic fermions can be clearly revealed by several perturbations, such as a uniform magnetic field, a Haldane-type spin-orbit term, and charge density waves. We comment on the possibility to probe the similarities and differences between the two kinds of relativistic fermions, or even to isolate them individually. We present a realistic scheme to realize such a system using cold atoms.

cond-mat.quant-gas↗

arXiv2012

Quantum entanglement of anharmonic oscillators

We investigate the quantum entanglement dynamics of undriven anharmonic (nonlinear) oscillators with quartic potentials. We first consider the indirect interaction between two such nonlinear oscillators mediated by a third, linear oscillator and show that it leads to a time-varying entanglement of the oscillators, the entanglement being strongly influenced by the nonlinear oscillator dynamics. In the presence of dissipation, the role of nonlinearity is strongly manifested in the steady state dynamics of the indirectly coupled anharmonic oscillators. We further illustrate the effect of nonlinearities by studying the coupling between an electromagnetic field in a cavity with one movable mirror which is modeled as a nonlinear oscillator. For this case we present a full analytical treatment, which is valid in a regime where both the nonlinearity and the coupling due to radiation pressure is weak. We show that, without the need of any conditional measurements on the cavity field, the state of the movable mirror is non-classical as a result of the combined effect of the intrinsic nonlinearity and the radiation pressure coupling. This interaction is also shown to be responsible for squeezing the movable mirror's position quadrature beyond the minimum uncertainty state even when the mirror is initially prepared in its ground state.

quant-ph↗

arXiv2012

Entanglement of distant optomechanical systems

We theoretically investigate the possibility to generate non-classical states of optical and mechanical modes of optical cavities, distant from each other. A setup comprised of two identical cavities, each with one fixed and one movable mirror and coupled by an optical fiber, is studied in detail. We show that with such a setup there is potential to generate entanglement between the distant cavities, involving both optical and mechanical modes. The scheme is robust with respect to dissipation, and nonlocal correlations are found to exist in the steady state at finite temperatures.

quant-ph↗

arXiv2008

Double and negative reflection of cold atoms in non-Abelian gauge potentials

Atom reflection is studied in the presence of a non-Abelian vector potential proportional to a spin-1/2 operator. The potential is produced by a relatively simple laser configuration for atoms with a tripod level scheme. We show that the atomic motion is described by two different dispersion branches with positive or negative chirality. As a consequence of that, atom reflection shows unusual features, since an incident wave may split into two reflected ones at a barrier, an ordinary specular reflection, and an additional non-specular one. Remarkably, the latter wave can exhibit negative reflection and may become evanescent if the angle of incidence exceeds a critical value. These reflection properties are crucial for future designs in non-Abelian atom optics.

cond-mat.other↗

arXiv2000

Quasi-periodic vs. irreversible dynamics of an optically confined Bose-Einstein condensate

We consider the evolution of a dilute Bose-Einstein condensate in an optical trap formed by a doughnut laser mode. By solving a one dimensional Gross-Pitaevskii equation and looking at the variance and the statistical entropy associated with the position of the system we can study the dynamical behavior of the system. It is shown that for small condensates nonlinear revivals of the macroscopic wave function are expected. For sufficiently large and dense condensates irreversible dynamics takes place for which revivals of regular dynamics appear as predicted in [9]. These results are confirmed by a two dimensional simulation in which the scales of energy associated with the two different directions mimic the experimental situation.

cond-mat.soft↗