arXiv subjects

Uwe R. Fischer

Publications and source records attributed to Uwe R. Fischer.

At least 37 records · Page 2Linked to original sources

arXiv2021

Benchmarking the multiconfigurational Hartree method by the exact wavefunction of two harmonically trapped bosons with contact interaction

We consider two bosons in a one-dimensional harmonic trap, interacting by a contact potential, and compare the exact solution of this problem to a self-consistent numerical solution by using the multiconfigurational time-dependent Hartree (MCTDH) method. We thereby benchmark the predictions of the MCTDH method with a few-body problem that has an analytical solution for the most commonly experimentally realized interaction potential in ultracold quantum gases. It is found that exact ground state energy and first order correlations are accurately reproduced by MCTDH up to the intermediate dimensionless coupling strengths corresponding to typical background scattering lengths of magnetically trapped ultracold dilute Bose gases. For larger couplings, established for example by (a combination of) Feshbach resonances and optical trapping, the MCTDH approach overestimates the depth of the trap-induced correlation dip of first order correlations in position space, as well as overestimates the fragmentation, defined as the average relative occupation of orbitals other than the energetically lowest one. We anticipate that qualitatively similar features in the correlation function may arise for larger particle numbers, paving the way for a quantitative assessment of the accuracy of MCTDH by experiments with ultracold atoms.

cond-mat.quant-gas↗

arXiv2021

Analogue gravitational field from nonlinear fluid dynamics

The dynamics of sound in a fluid is intrinsically nonlinear. We derive the consequences of this fact for the analogue gravitational field experienced by sound waves, by first describing generally how the nonlinearity of the equation for phase fluctuations back-reacts onto the definition of the background providing the effective space-time metric. Subsequently, we use the the analytical tool of Riemann invariants in one-dimensional motion to derive source terms of the effective gravitational field stemming from nonlinearity. Finally, we show that the consequences of nonlinearity we derive can be observed with Bose-Einstein condensates in the ultracold gas laboratory.

gr-qc↗

arXiv2020

Verifying the upper bound on the speed of scrambling with the analogue Hawking radiation of trapped ions

A general bound on the Lyapunov exponent of a quantum system is given by $λ_L\leq2π\,T/\hbar$, where $T$ is the system temperature, as established by Maldacena, Shenker, and Stanford (MSS). This upper bound is saturated when the system under consideration is the exact holographic dual of a black hole. It has also been shown that an inverted harmonic oscillator (IHO) may exhibit the behavior of thermal energy emission, in close analogy to the Hawking radiation emitted by black holes. We demonstrate that the Lyapunov exponent of the IHO indeed saturates the MSS bound, with an effective temperature equal to the analogue black hole radiation temperature, and propose using a trapped ion as a physical implementation of the IHO. We derive the corresponding out-of-time-ordered correlation function (OTOC) diagnosing quantum chaos, and theoretically show, for an experimentally realizable setup, that the effective temperature of the trapped-ion-IHO matches the upper MSS bound for the speed of scrambling.

quant-ph↗

arXiv2020

Stoner-Wohlfarth switching of the condensate magnetization in a dipolar spinor gas and the metrology of excitation damping

We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in the homogeneous-local-spin-orientation approximation, that is with unidirectional local magnetization. By analytically calculating the exact effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert equation for the dissipative condensate magnetization dynamics, and show how it leads to the Stoner-Wohlfarth model of a uni-axial ferro-magnetic particle, where the latter model determines the stable magnetization patterns and hysteresis curves for switching between them. For an external magnetic field pointing along the axial, long direction, we analytically solve the Landau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that the magnetic dipole-dipole interaction {\it accelerates} the dissipative dynamics of the magnetic moment distribution and the associated dephasing of the magnetic moment direction. Under suitable conditions, dephasing of the magnetization direction due to dipole-dipole interactions occurs within time scales up to two orders of magnitude smaller than the lifetime of currently experimentally realized dipolar spinor condensates, e.g., produced with the large magnetic-dipole-moment atoms ${}^{166} \textrm{Er}$. This enables experimental access to the dissipation parameter $Γ$ in the Gross-Pitaevski\vı~mean-field equation, for a system currently lacking a complete quantum kinetic treatment of dissipative processes and, in particular, an experimental check of the commonly used assumption that $Γ$ is a single scalar independent of spin indices.

cond-mat.quant-gas↗

arXiv2019

Exact surface-wave spectrum of a dilute quantum liquid

We consider a dilute gas of bosons with repulsive contact interactions, described on the mean-field level by the Gross-Pitaevskii equation, and bounded by an impenetrable "hard" wall (either rigid or flexible). We solve the Bogoliubov-de Gennes equations for excitations on top of the Bose-Einstein condensate analytically, by using matrix-valued hypergeometric functions. This leads to the exact spectrum of gapless Bogoliubov excitations localized near the boundary. The dispersion relation for the surface excitations represents for small wavenumbers $k$ a ripplon mode with fractional power law dispersion for a flexible wall, and a phonon mode (linear dispersion) for a rigid wall. For both types of excitation we provide, for the first time, the exact dispersion relations of the dilute quantum liquid for all $k$ along the surface, extending to $k \rightarrow \infty$. The small wavelength excitations are shown to be bound to the surface with a maximal binding energy $Δ= \frac18 (\sqrt{17}-3)^2 mc^2 \simeq 0.158\, mc^2$, which both types of excitation asymptotically approach, where $m$ is mass of bosons and $c$ bulk speed of sound. We demonstrate that this binding energy is close to the experimental value obtained for surface excitations of helium II confined in nanopores, reported in Phys. Rev. B 88, 014521 (2013).

cond-mat.quant-gas↗

arXiv2019

Many-body quantum metrology with scalar bosons in a single potential well

We theoretically investigate the possibility of performing high precision estimation of an externally imposed acceleration using scalar bosons in a single-well trap. We work at the level of a two-mode truncation, valid for weak to intermediate two-body interaction couplings.The splitting process into two modes is in our model entirely caused by the interaction between the constituent bosons and is hence neither due to an externally imposed double-well potential nor due to populating a spinor degree of freedom. The precision enhancement gained by using various initial quantum states using a two-mode bosonic system is well established. Here we therefore instead focus on the effect of the intrinsic dynamics on the precision, where, in a single well, the Hamiltonian assumes a form different from that of the typical double-well case. We demonstrate how interactions can significantly increase the quantum Fisher information maximized over initial states as well as the quantum Fisher information for a fragmented or a coherent state, the two many-body states that can commonly represent the ground state of our system.

quant-ph↗

arXiv2019

Self-consistent determination of the many-body state of ultracold bosonic atoms in a one-dimensional harmonic trap

We study zero-temperature quantum fluctuations in harmonically trapped one-dimensional interacting Bose gases, using the self-consistent multiconfigurational time-dependent Hartree method. We define $phase$ $fluctuations$ from the full single-particle density matrix by the spatial decay exponent of off-diagonal long-range order. In a regime of mesoscopic particle numbers and moderate contact couplings, we derive the spatial dependence of the amplitude of phase fluctuations, determined from the {\em self-consistently} derived shape of the field operator orbitals and Fock space orbital occupation amplitudes. It is shown that the phase fluctuations display a peak, which in turn corresponds to a dip of the first-order correlations in position space, akin to what has previously been obtained in the Tonks-Girardeau limit of very large interactions and low densities.

cond-mat.quant-gas↗

arXiv2018

Implementation-independent sufficient condition of the Knill-Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation

Autonomous quantum error correction utilizes the engineered coupling of a quantum system to a dissipative ancilla to protect quantum logical states from decoherence. We show that the Knill-Laflamme condition, stating that the environmental error operators should act trivially on a subspace, which then becomes the code subspace, is sufficient for logical qudits to be protected against Markovian noise. It is proven that the error caused by the total Lindbladian evolution in the code subspace can be suppressed up to very long times in the limit of large engineered dissipation, by explicitly deriving how the error scales with both time and engineered dissipation strength. To demonstrate the potential of our approach for applications, we implement our general theory with binomial codes, a class of bosonic error-correcting codes, and outline how they can be implemented in a fully autonomous manner to protect against photon loss in a microwave cavity.

quant-ph↗

arXiv2018

Roton entanglement in quenched dipolar Bose-Einstein condensates

We study quasi-two-dimensional dipolar Bose-Einstein condensates, in which the Bogoliubov excitation spectrum displays, at sufficiently large gas density, a deep roton minimum due to the spatially anisotropic behavior of the dipolar two-body potential. A rapid quench, performed on the speed of sound of excitations propagating on the condensate background, leads to the dynamical Casimir effect, which can be characterized by measuring the density-density correlation function. It is shown, for both zero and finite initial temperatures, that the continuous-variable bipartite quantum state of the created quasiparticle pairs with opposite momenta, resulting from the quench, displays an enhanced potential for the presence of entanglement (represented by nonseparable and steerable quasiparticle states), when compared to a gas with solely repulsive contact interactions. Steerable quasiparticle pairs contain momenta from close to the roton, and hence quantum correlations significantly increase in the presence of a deep roton minimum.

quant-ph↗

arXiv2018

Mesoscopics of half-quantum vortex pair deconfinement in a trapped spin-one condensate

Motivated by a recent experiment in an antiferromagnetic spin-1 Bose-Einstein condensate of ${}^{23} \textrm{Na}$ atoms, we study the energetical stability of a singly quantum vortex injected into the center of a quasi-two-dimensional gas with zero total spin against dissocation into a pair of half-quantum vortices. We find that the critical dissociation point of this confinement-deconfinement type phase transition can be expressed in terms of the ratio of density-density ($c_0$) and spin-spin ($c_2$) coupling constants. The transition of bound to unbound vortices, in particular, sensitively depends on (1) the ratio of system size ($R$) to density healing length ($ξ_d$), and (2) the trap potential. Specifically, the critical ratio $(c_2 / c_0)_{\textrm{cr}}$ increases when $R / ξ_d$ decreases, and is relatively larger in a harmonic trap than in a box trap. Dissociation is energetically generally favored for $c_2 / c_0 < (c_2 / c_0)_{\textrm{cr}}$, which as a corollary implies that vortex dissociation is observed as well for negative $c_2 < 0$, e.g., in a rubidium spin-1 BEC, whereas in a sodium spin-1 BEC ($c_2>0$) it is energetically blocked above the critical ratio $(c_2 / c_0)_{\textrm{cr}}$. Tuning the coupling ratio $c_2/c_0$ by using microwave control techniques, the dependence of the deconfinement phase transition on coupling parameters, density, and system size we predict, can be verified in experiments with ultracold spinor gases.

cond-mat.quant-gas↗

arXiv2017

Intrinsic measurement errors for the speed of light in vacuum

The speed of light in vacuum, one of the most important and precisely measured natural constants, is fixed by convention to $c=299 792 458$ m/s. Advanced theories predict possible deviations from this universal value, or even quantum fluctuations of $c$. Combining arguments from quantum parameter estimation theory and classical general relativity, we here establish rigorously the existence of lower bounds on the uncertainty to which the speed of light in vacuum can be determined in a given region of space-time, subject to several reasonable restrictions. They provide a novel perspective on the experimental falsifiability of predictions for the quantum fluctuations of space-time.

quant-ph↗

arXiv2017

Probing the scale invariance of the inflationary power spectrum in expanding quasi-two-dimensional dipolar condensates

We consider an analogue de Sitter cosmos in an expanding quasi-two-dimensional Bose-Einstein condensate with dominant dipole-dipole interactions between the atoms or molecules in the ultracold gas. It is demonstrated that a hallmark signature of inflationary cosmology, the scale invariance of the power spectrum of inflaton field correlations, experiences strong modifications when, at the initial stage of expansion, the excitation spectrum displays a roton minimum. Dipolar quantum gases thus furnish a viable laboratory tool to experimentally investigate, with well-defined and controllable initial conditions, whether primordial oscillation spectra deviating from Lorentz invariance at trans-Planckian momenta violate standard predictions of inflationary cosmology.

cond-mat.quant-gas↗

arXiv2016

Amplification of the quantum superposition macroscopicity of a flux qubit by a magnetized Bose gas

We calculate a measure of superposition macroscopicity $\mathcal{M}$ for a superposition of screening current states in a superconducting flux qubit (SFQ), by relating $\mathcal{M}$ to the action of an instanton trajectory connecting the potential wells of the flux qubit. When a magnetized Bose-Einstein condensed (BEC) gas containing $N_{B}\sim \mathcal{O}(10^6)$ atoms is brought into a $\mathcal{O}(1)$ $μ\text{m}$ proximity of the flux qubit in an experimentally realistic geometry, we demonstrate the appearance of a two- to five-fold amplification of $\mathcal{M}$ over the bare value without the BEC, by calculating the instantion trajectory action from the microscopically derived effective flux Lagrangian of a hybrid quantum system composed of the flux qubit and a spin-$F$ atomic Bose gas. Exploiting the connection between $\mathcal M$ and the maximal metrological usefulness of a multimode superposition state, we show that amplification of $\mathcal{M}$ in the ground state of the hybrid system is equivalent to a decrease in the quantum Cramér-Rao bound for estimation of an externally applied flux. Our result therefore demonstrates the increased usefulness of the BEC--SFQ hybrid system as a sensor of ultraweak magnetic fields below the standard quantum limit.

quant-ph↗

arXiv2016

Quantum sine-Gordon dynamics on analogue curved spacetime in a weakly imperfect scalar Bose gas

Using the coherent state functional integral expression of the partition function, we show that the sine-Gordon model on an analogue curved spacetime arises as the effective quantum field theory for phase fluctuations of a weakly imperfect Bose gas on an incompressible background superfluid flow when these fluctuations are restricted to a subspace of the single-particle Hilbert space. We consider bipartitions of the single-particle Hilbert space relevant to experiments on ultracold bosonic atomic or molecular gases, including, e.g., restriction to high- or low-energy sectors of the dynamics and spatial bipartition corresponding to tunnel-coupled planar Bose gases. By assuming full unitary quantum control in the low-energy subspace of a trapped gas, we show that (1) appropriately tuning the particle number statistics of the lowest-energy mode partially decouples the low- and high-energy sectors, allowing any low-energy single-particle wave function to define a background for sine-Gordon dynamics on curved spacetime and (2) macroscopic occupation of a quantum superposition of two states of the lowest two modes produces an analogue curved spacetime depending on two background flows, with respective weights continuously dependent on the corresponding weights of the superposed quantum states.

quant-ph↗

arXiv2016

"Photonic" cat states from strongly interacting matter waves

We consider ultracold quantum gases of scalar bosons, residing in a coupling strength--density regime in which they constitute a twofold fragmented condensate trapped in a single well. It is shown that the corresponding quantum states are, in the appropriate Fock space basis, identical to the photon cat states familiar in quantum optics, which correspond to superpositions of coherent states of the light field with a phase difference of $π$. In marked distinction to photon cat states, the very existence of matter wave cat states however crucially depends on the many-body correlations of the constituent particles. We consequently establish that the quadratures of the effective "photons," expressing the highly nonclassical nature of the macroscopic matter wave superposition state, can be experimentally accessed by measuring the density-density correlations of the interacting quantum gas.

quant-ph↗

arXiv2015

Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions

The occupation of more than one single-particle state and hence the emergence of fragmentation is a many-body phenomenon universal to systems of spatially confined interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems. We solve the full many-body Schrödinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density and interaction strength is assessed. It is found that for contact interactions, the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long-ranged the interactions become. The degree of fragmentation is increasing, keeping the particle number $N$ fixed, when the density is decreasing as expected in one spatial dimension. We demonstrate that this remains, nontrivially, true also for long-range interactions in two spatial dimensions. We, finally, find that within our fully self-consistent approach, the fragmentation degree, to a good approximation, decreases universally as $N^{-1/2}$ when only $N$ is varied.

cond-mat.quant-gas↗

arXiv2014

Consistent perturbative treatment of the subohmic spin-boson model yielding arbitrarily small $T_2/T_1$ decoherence time ratios

We present a perturbative treatment of the subohmic spin-boson model which remedies a crucial flaw in previous treatments. The problem is traced back to the incorrect application of a Markov type approximation to specific terms in the temporal evolution of the reduced density matrix. The modified solution is consistent both with numerical simulations and the exact solution obtained when the bath-coupling spin-space direction is parallel to the qubit energy-basis spin. We therefore demonstrate that %in distinction to previous findings the subohmic spin-boson model is capable of %consistently describing arbitrarily small %(less than two) ratios of the $T_2$ and $T_1$ decoherence times, associated to the decay of the off-diagonal and diagonal reduced density-matrix elements, respectively. An analytical formula for $T_2/T_1$ at the absolute zero of temperature is provided in the limit of a subohmic bath with vanishing spectral power law exponent. Small ratios closely mimic the experimental results for solid state (flux) qubits, which are subject predominantly to low-frequency electromagnetic noise, and we suggest a reanalysis of the corresponding experimental data in terms of a $nonanalytic$ decay of off-diagonal coherence.

cond-mat.mes-hall↗

arXiv2014

Truncated many-body dynamics of interacting bosons: A variational principle with error monitoring

We develop a method to describe the temporal evolution of an interacting system of bosons, for which the field operator expansion is truncated after a finite number $M$ of modes, in a rigorously controlled manner. Using McLachlan's principle of least error, we find a self-consistent set of equations for the many-body state. As a particular benefit, and in distinction to previously proposed approaches, the presently introduced method facilitates the dynamical increase of the number of orbitals during the temporal evolution, due to the fact that we can rigorously monitor the error made by increasing the truncation dimension $M$. The additional orbitals, determined by the condition of least error of the truncated evolution relative to the exact one, are obtained from an initial trial state by steepest $constrained$ descent.

cond-mat.quant-gas↗