arXiv subjects

Martin Holthaus

Publications and source records attributed to Martin Holthaus.

At least 19 recordsLinked to original sources

arXiv2025

Pre-Floquet states facilitating coherent subharmonic response of periodically driven many-body systems

We demonstrate longtime coherent subharmonic motion of a many-boson system subjected to an external time-periodic driving force. The underlying mechanism is exemplified numerically through analysis of a periodically driven Bose-Hubbard dimer, and clarified conceptually by semiclassical requantization of invariant tubes pertaining to the system's mean-field description. In this way, one arrives at pre-Floquet states that relate to the actual many-body Floquet states in a manner similar to the relation of site-localized Wannier states to lattice-extended Bloch states in solid-state physics. It is argued that even high-order subharmonic response can be systematically engineered, and be observed experimentally, with weakly interacting Floquet condensates comprising a sufficiently large number of particles.

quant-ph↗

arXiv2025

Degree of simplicity of Floquet states of a periodically driven Bose-Hubbard dimer

We investigate numerically computed Floquet states of a Bose-Hubbard dimer which is subjected to strong, time-periodic forcing with respect to their coherence, invoking a measure for their degree of simplicity previously suggested by Leggett. This serves to ascertain the validity of the mean-field approximation under conditions such that the time-dependent nonlinear Gross-Pitaevskii equation has chaotic solutions. It is shown that for sufficiently large particle numbers the exact N-particle Floquet state semiclassically associated with the innermost quantized invariant tube surrounding a stable periodic mean-field orbit represents a macroscopically occupied single-particle state, i.e., a Floquet condensate.

quant-ph↗

arXiv2024

Wave packet dynamics in parabolic optical lattices: From Bloch oscillations to long-range dynamical tunneling

We investigate the dynamics of wave packets in a parabolic optical lattice formed by combining an optical lattice with a global parabolic trap. Our study examines the phase space representation of the system's eigenstates by comparing them to the classical phase space of a pendulum, to which the system effectively maps. The analysis reveals that quantum states can exhibit mixed dynamics by straddling the separatrix. A key finding is that the dynamics around the separatrix enables the controlled creation of highly non-classical states, distinguishing them from the classical oscillatory or rotational dynamics of the pendulum. By considering a finite momentum of the initial wave packet, we demonstrate various dynamical regimes. Furthermore, a slight energy mismatch between nearly-degenerate states localized at opposite turning points of the trap potential results in controlled long-range dynamical tunneling. These results can be interpreted as quantum beating between a clockwise rotating and a counterclockwise rotating pendulum.

quant-ph↗

arXiv2024

Floquet dynamics of ultracold atoms in optical lattices with a parametrically modulated trapping potential

Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum-classical correspondence.

cond-mat.quant-gas↗

arXiv2023

Chirped Bloch-Harmonic oscillations in a parametrically forced optical lattice

The acceleration theorem for wavepacket propagation in periodic potentials disentangles the kspace dynamics and real-space dynamics. This is well known and understood for Bloch oscillations and super Bloch oscillations in the presence of position-independent forces. Here, we analyze the dynamics of a model system in which the k-space dynamics and the real-space dynamics are inextricably intertwined due to a position-dependent force which is provided by a parabolic trap. We demonstrate that this coupling gives rise to significantly modified and rich dynamics when the lattice is shaken by a modulated parabolic potential. The dynamics range from chirped Bloch-Harmonic oscillations to the asymmetric spreading oscillations. We analyze these findings by tracing the spatio-temporal dynamics in real space and by visualizing the relative phase in the k-space dynamics which leads to an accurate explanation of the obtained phenomena. We also compare our numerical results to a local acceleration model and obtain very good agreement for the case of coherent oscillations, however, deviations for oscillations with spreading dynamics which altogether supports the interpretations of our findings.

quant-ph↗

arXiv2021

Following Floquet states in high-dimensional Hilbert spaces

An iterative algorithm is established which enables one to compute individual Floquet states even for many-body systems with high-dimensional Hilbert spaces that are not accessible to commonly employed conventional methods. A strategy is proposed for following a Floquet state in response to small changes of a given system's Hamiltonian. The scheme is applied to a periodically driven Bose-Hubbard chain, verifying the possibility of pseudoadiabatic Floquet state following. In particular, it is demonstrated that a driving-induced Mott insulatorlike target Floquet state can be populated with high efficiency if the driving amplitude is turned on smoothly but not too slowly. We conclude that the algorithm constitutes a powerful tool for the future investigation of many-body Floquet systems.

cond-mat.quant-gas↗

arXiv2020

Environment-controlled Floquet-state paramagnetism

We study the response of ideal spin systems which are interacting with both a strong oscillating magnetic field, and a thermal environment, to a weak probing magnetic field. We demonstrate that even the sign of the resulting mean magnetization depends on the amplitude of the driving field, and that its absolute value can be significantly larger than the equilibrium magnetization in the absence of time-periodic forcing. Since the underlying Floquet-state occupation probabilities are determined by the precise form of the system-bath coupling, future measurements of such effects have the potential to establish a particularly innovative line of research, providing information on nonequilibrium thermodynamics, and giving access to quantities which usually remain hidden when probing equilibrium systems.

quant-ph↗

arXiv2019

Quantum critical properties of Bose-Hubbard models

The Mott insulator-to-superfluid transition exhibited by the Bose-Hubbard model on a two-dimensional square lattice occurs for any value of the chemical potential, but becomes critical at the tips of the so-called Mott lobes only. Employing a numerical approach based on a combination of high-order perturbation theory and hypergeometric analytic continuation we investigate how quantum critical properties manifest themselves in computational practice. We consider two-dimensional triangular lattices and three-dimensional cubic lattices for comparison, providing accurate parametrizations of the phase boundaries at the tips of the respective first lobes. In particular, we lend strong support to a recently suggested inequality which bounds the divergence exponent of the one-particle correlation function in terms of that of the two-particle correlation function, and which sharpens to an equality if and only if a system becomes critical.

cond-mat.stat-mech↗

arXiv2019

Floquet-state cooling

We demonstrate that a periodically driven quantum system can adopt a quasistationary state which is effectively much colder than a thermal reservoir it is coupled to, in the sense that certain Floquet states of the driven-dissipative system can carry much higher population than the ground state of the corresponding undriven system in thermal equilibrium. This is made possible by a rich Fourier spectrum of the system's Floquet transition matrix elements, the components of which are addressed individually by a suitably peaked reservoir density of states. The effect is expected to be important for driven solid-state systems interacting with a phonon bath predominantly at well-defined frequencies.

quant-ph↗

arXiv2019

Periodic thermodynamics of the parametrically driven harmonic oscillator

We determine the quasistationary distribution of Floquet-state occupation probabilities for a parametrically driven harmonic oscillator coupled to a thermal bath. Since the system exhibits detailed balance, and the canonical representatives of its quasienergies are equidistant, these probabilities are given by a geometrical Boltzmann distribution, but its quasitemperature differs from the actual temperature of the bath, being affected by the functional form of the latter's spectral density. We provide two examples of quasithermal engineering, i.e., of deliberate manipulation of the quasistationary distribution by suitable design of the spectral density: We show that the driven system can effectively be made colder than the undriven one, and demonstrate that quasithermal instability can occur even when the system is mechanically stable.

quant-ph↗

arXiv2019

Periodic thermodynamics of the Rabi model with circular polarization for arbitrary spin quantum numbers

We consider a spin $s$ subjected to both a static and an orthogonally applied oscillating, circularly polarized magnetic field while being coupled to a heat bath, and analytically determine the quasi\-stationary distribution of its Floquet-state occupation probabilities for arbitrarily strong driving. This distribution is shown to be Boltzmannian with a quasitemperature which is different from the temperature of the bath, and independent of the spin quantum number. We discover a remarkable formal analogy between the quasithermal magnetism of the nonequilibrium steady state of a driven ideal paramagnetic material, and the usual thermal paramagnetism. Nonetheless, the response of such a material to the combined fields is predicted to show several unexpected features, even allowing one to turn a paramagnet into a diamagnet under strong driving. Thus, we argue that experimental measurements of this response may provide key paradigms for the emerging field of periodic thermodynamics.

quant-ph↗

arXiv2018

Floquet theory of the analytical solution of a periodically driven two-level system

We investigate the analytical solution of a two-level system subject to a monochromatical, linearly polarized external field that was published a couple of years ago. In particular, we derive an explicit expression for the quasienergy. Moreover, we calculate the time evolution of a typical two-level system over a full period by evaluating series solutions of the confluent Heun equation. This is possible without invoking the connection problem of this equation since the complete time evolution of the system under consideration can be reduced to that of the first quarter-period.

quant-ph↗

arXiv2018

Hypergeometric continuation of divergent perturbation series. I. Critical exponents of the Bose-Hubbard model

We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional $XY$ universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.

cond-mat.stat-mech↗

arXiv2018

Hypergeometric continuation of divergent perturbation series. II. Comparison with Shanks transformation and Padé approximation

We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose-Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions.

cond-mat.stat-mech↗

arXiv2016

Adiabatic preparation of Floquet condensates

We argue that a Bose-Einstein condensate can be transformed into a Floquet condensate, that is, into a periodically time-dependent many-particle state possessing the coherence properties of a mesoscopically occupied single-particle Floquet state. Our reasoning is based on the observation that the denseness of the many-body system's quasienergy spectrum does not necessarily obstruct effectively adiabatic transport. Employing the idealized model of a driven bosonic Josephson junction, we demonstrate that only a small amount of Floquet entropy is generated when a driving force with judiciously chosen frequency and maximum amplitude is turned on smoothly.

cond-mat.quant-gas↗

arXiv2016

Entropy production within a pulsed Bose-Einstein condensate

We suggest to subject anharmonically trapped Bose-Einstein condensates to sinusoidal forcing with a smooth, slowly changing envelope, and to measure the coherence of the system after such pulses. In a series of measurements with successively increased maximum forcing strength one then expects an adiabatic return of the condensate to its initial state as long as the pulses remain sufficiently weak. In contrast, once the maximum driving amplitude exceeds a certain critical value there should be a drastic loss of coherence, reflecting significant heating induced by the pulse. This predicted experimental signature is traced to the loss of an effective adiabatic invariant, and to the ensuing breakdown of adiabatic motion of the system's Floquet state when the many-body dynamics become chaotic. Our scenario is illustrated with the help of a two-site model of a forced bosonic Josephson junction, but should also hold for other, experimentally accessible configurations.

cond-mat.quant-gas↗

arXiv2015

Floquet engineering with quasienergy bands of periodically driven optical lattices

A primer on the Floquet theory of periodically time-dependent quantum systems is provided, and it is shown how to apply this framework for computing the quasienergy band structure governing the dynamics of ultracold atoms in driven optical cosine lattices. Such systems are viewed here as spatially and temporally periodic structures living in an extended Hilbert space, giving rise to spatio-temporal Bloch waves whose dispersion relations can be manipulated at will by exploiting ac-Stark shifts and multiphoton resonances. The elements required for numerical calculations are introduced in a tutorial manner, and some example calculations are discussed in detail, thereby illustrating future prospects of Floquet engineering.

quant-ph↗

arXiv2015

$N$-coherence vs. $t$-coherence: An alternative route to the Gross-Pitaevskii equation

We show how a candidate mean-field amplitude can be constructed from the exact wave function of an externally forced $N$-Boson system. The construction makes use of subsidiary $(N-1)$-particle states which are propagated in time in addition to the true $N$-particle state, but does not involve spontaneous breaking of the $U(1)$ symmetry associated with particle number conservation. Provided the flow in Fock space possesses a property which we call maximum stiffness, or $t$-coherence, the candidate amplitude actually satisfies the time-dependent Gross-Pitaevskii equation, and then serves as macroscopic wave function of the forced $N$-particle system. The general procedure is illustrated in detail by numerical calculations performed for the model of a driven bosonic Josephson junction, which allows one to keep track of all contributions which usually are subject to uncontrolled assumptions. These calculations indicate that macroscopic wave functions can persist even under conditions of strong forcing, but are rapidly destroyed upon entering a regime of chaotic dynamics. Our results provide a foundation for future attempts to manipulate, and actively control, macroscopic wave functions by means of purposefully designed force protocols.

cond-mat.quant-gas↗