arXiv subjects

Michael Uhlmann

Publications and source records attributed to Michael Uhlmann.

14 recordsLinked to original sources

arXiv2010

Time-resolved density correlations as probe of squeezing in toroidal Bose-Einstein condensates

I study the evolution of mean field and linear quantum fluctuations in a toroidal Bose-Einstein condensate, whose interaction strength is quenched from a finite (repulsive) value to zero. The azimuthal equal-time density-density correlation function is calculated and shows temporal oscillations with twice the (final) excitation frequencies after the transition. These oscillations are a direct consequence of positive and negative frequency mixing during non-adiabatic evolution. I will argue that a time-resolved measurement of the equal-time density correlator might be used to calculate the moduli of the Bogoliubov coefficients and thus the amount of squeezing imposed on a mode, i.e., the number of atoms excited out of the condensate.

cond-mat.quant-gas↗

arXiv2010

System size scaling of topological defect creation in a second-order dynamical quantum phase transition

We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for large N, we find that the net defect number variance in convex volumina scales like the surface area of the sample for short-range correlations. This behaviour follows generally from spatial and internal symmetries. Conversely, if spatial isotropy is broken, e.g., by a lattice, and in addition long-range periodic correlations develop in the broken-symmetry phase, we get the rather counterintuitive result that the scaling strongly depends on the dimension being even or odd: For even dimensions, the net defect number variance scales like the surface area squared, with a prefactor oscillating with the system size, while for odd dimensions, it essentially vanishes.

cond-mat.stat-mech↗

arXiv2010

O(N) symmetry-breaking quantum quench: Topological defects versus quasiparticles

We present an analytical derivation of the winding number counting topological defects created by an O(N) symmetry-breaking quantum quench in N spatial dimensions. Our approach is universal in the sense that we do not employ any approximations apart from the large-$N$ limit. The final result is nonperturbative in N, i.e., it cannot be obtained by %the usual an expansion in 1/N, and we obtain far less topological defects than quasiparticle excitations, in sharp distinction to previous, low-dimensional investigations.

cond-mat.stat-mech↗

arXiv2008

Quantum fluctuations in trapped time-dependent Bose-Einstein condensates

Quantum fluctuations in time-dependent, harmonically-trapped Bose-Einstein condensates are studied within Bogoliubov theory. An eigenmode expansion of the linear field operators permits the diagonalization of the Bogoliubov-de Gennes equation for a stationary condensate. When trap frequency or interaction strength are varied, the inhomogeneity of the background gives rise to off-diagonal coupling terms between different modes. This coupling is negligible for low energies, i.e., in the hydrodynamic regime, and an effective space-time metric can be introduced. The influence of the inter-mode coupling will be demonstrated in an example, where I calculate the quasi-particle number for a quasi-one-dimensional Bose-Einstein condensate subject to an exponential sweep of interaction strength and trap frequency.

cond-mat.other↗

arXiv2008

Effect of fluctuations on the superfluid-supersolid phase transition on the lattice

We derive a controlled expansion into mean field plus fluctuations for the extended Bose-Hubbard model, involving interactions with many neighbors on an arbitrary periodic lattice, and study the superfluid-supersolid phase transition. Near the critical point, the impact of (thermal and quantum) fluctuations on top of the mean field grows, which entails striking effects, such as negative superfluid densities and thermodynamical instability of the superfluid phase -- earlier as expected from mean-field dynamics. We also predict the existence of long-lived "supercooled" states with anomalously large quantum fluctuations.

cond-mat.other↗

arXiv2008

Bogoliubov theory of quantum correlations in the time-dependent Bose-Hubbard model

By means of an adapted mean-field expansion for large fillings $n\gg1$, we study the evolution of quantum fluctuations in the time-dependent Bose-Hubbard model, starting in the superfluid state and approaching the Mott phase by decreasing the tunneling rate or increasing the interaction strength in time. For experimentally relevant cases, we derive analytical results for the temporal behavior of the number and phase fluctuations, respectively. This allows us to calculate the growth of the quantum depletion and the decay of off-diagonal long-range order. We estimate the conditions for the observability of the time dependence in the correlation functions in the experimental setups with external trapping present. Finally, we discuss the analogy to quantum effects in the early universe during the inflationary epoch.

cond-mat.other↗

arXiv2007

Vortex quantum creation and winding number scaling in a quenched spinor Bose gas

Motivated by a recent experiment, we study non-equilibrium quantum phenomena taking place in the quench of a spinor Bose-Einstein condensate through the zero-temperature phase transition separating the polar paramagnetic and planar ferromagnetic phases. We derive the typical spin domain structure (correlations of the effective magnetization) created by the quench arising due to spin-mode quantum fluctuations, and establish a sample-size scaling law for the creation of spin vortices, which are topological defects in the transverse magnetization.

cond-mat.other↗

arXiv2007

Analogue of cosmological particle creation in an ion trap

We study phonons in a dynamical chain of ions confined by a trap with a time-dependent (axial) potential strength and demonstrate that they behave in the same way as quantum fields in an expanding/contracting universe. Based on this analogy, we present a scheme for the detection of the analogue of cosmological particle creation which should be feasible with present-day technology. In order to test the quantum nature of the particle creation mechanism and to distinguish it from classical effects such as heating, we propose to measure the two-phonon amplitude via the $2^{\rm nd}$ red side-band and to compare it with the one-phonon amplitude ($1^{\rm st}$ red side-band). PACS: 04.62.+v, 98.80.-k, 42.50.Vk, 32.80.Pj.

quant-ph↗

arXiv2006

Sweeping from the superfluid to Mott phase in the Bose-Hubbard model

We study the sweep through the quantum phase transition from the superfluid to the Mott state for the Bose-Hubbard model with a time-dependent tunneling rate $J(t)$. In the experimentally relevant case of exponential decay, $J(t)\propto e^{-γt}$, an adapted mean-field expansion for large fillings $n$ yields a scaling solution for the fluctuations. This enables us to analytically calculate the evolution of the number and phase variations (on-site) and correlations (off-site) for slow ($γ\llμ$), intermediate, and fast (non-adiabatic $γ\ggμ$) sweeps, where $μ$ is the chemical potential. Finally, we derive the dynamical decay of the off-diagonal long-range order as well as the temporal shrinkage of the superfluid fraction in a persistent ring-current setup.

cond-mat.stat-mech↗

arXiv2006

Signatures of Planck-scale interactions in the cosmic microwave background?

Based on a rather general low-energy effective action (interacting quantum fields in classical curved space-times), we calculate potential signatures of new physics (such as quantum gravity) at ultra-high energies (presumably the Planck scale) in the anisotropies of the cosmic microwave background. These Planck-scale interactions create non-Gaussian contributions, where special emphasis is laid on the three-point function as the most promising observable, which also allows the discrimination between models violating and those obeying Lorentz invariance. PACS: 98.80.Cq, 04.62.+v, 98.70.Vc, 98.80.Qc.

gr-qc↗

arXiv2005

Quantum backreaction in dilute Bose-Einstein condensates

For many physical systems which can be approximated by a classical background field plus small (linearized) quantum fluctuations, a fundamental question concerns the correct description of the backreaction of the quantum fluctuations onto the dynamics of the classical background. We investigate this problem for the example of dilute atomic/molecular Bose-Einstein condensates, for which the microscopic dynamical behavior is under control. It turns out that the effective-action technique does not yield the correct result in general and that the knowledge of the pseudo-energy-momentum tensor ${<\hat T_{μν}>}$ is not sufficient to describe quantum backreaction.

cond-mat.other↗

arXiv2005

Mean-field expansion in Bose-Einstein condensates with finite-range interactions

We present a formal derivation of the mean-field expansion for dilute Bose-Einstein condensates with two-particle interaction potentials which are weak and finite-range, but otherwise arbitrary. The expansion allows for a controlled investigation of the impact of microscopic interaction details (e.g., the scaling behavior) on the mean-field approach and the induced higher-order corrections beyond the s-wave scattering approximation.

cond-mat.other↗

arXiv2005

Aspects of Cosmic Inflation in Expanding Bose-Einstein Condensates

Phonons in expanding Bose-Einstein condensates with wavelengths much larger than the healing length behave in the same way as quantum fields within a universe undergoing an accelerated expansion. This analogy facilitates the application of many tools and concepts known from general relativity (such as horizons) and the prediction of the corresponding effects such as the freezing of modes after horizon crossing and the associated amplification of quantum fluctuations. Basically the same amplification mechanism is (according to our standard model of cosmology) supposed to be responsible for the generation of the initial inhomogeneities -- and hence the seeds for the formation of structures such as our galaxy -- during cosmic inflation (i.e., a very early epoch in the evolution of our universe). After a general discussion of the analogy (\emph{analogue cosmology}), we calculate the frozen and amplified density-density fluctuations for quasi-two dimensional (Q2D) and three dimensional (3D) condensates which undergo a free expansion after switching off the (longitudinal) trap. PACS: 03.75.Kk, 04.62.+v.

quant-ph↗

arXiv2004

Resonant cavity photon creation via the dynamical Casimir effect

Motivated by a recent proposal for an experimental verification of the dynamical Casimir effect, the macroscopic electromagnetic field within a perfect cavity containing a thin slab with a time-dependent dielectric permittivity is quantized in terms of the dual potentials. For the resonance case, the number of photons created out of the vacuum due to the dynamical Casimir effect is calculated for both polarizations (TE and TM). PACS: 42.50.Lc, 03.70.+k, 42.50.Dv, 42.60.Da.

quant-ph↗