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C. E. Creffield

Publications and source records attributed to C. E. Creffield.

At least 19 recordsLinked to original sources
arXiv2022

Expansion of a one-dimensional Bose gas: the role of interactions and kinetic-energy driving

We study the expansion of a one-dimensional boson gas by suddenly increasing the length of the chain where it resides. We consider three initial ground-state configurations: the Mott insulator, the conventional superfluid clumped around zero momentum, and the cat-like state with peaks at momenta $\pm π/2$, resulting from rapid kinetic driving. In turn, we consider three types of expansion: spectroscopic (with interactions tuned to zero), dynamic (with standard short-range repulsive interactions) and under kinetic driving. The numerical calculations are exact. We compute the momentum- and real-space one-particle densities as well as the two-particle momentum correlations. The spectroscopic time-of-flight experiment faithfully reflects the initial momentum distribution. For the dynamic expansion starting from an insulator, we reproduce the non-equilibrium quasi-condensation into momenta $\pm π/2$ while noticing correlations in the momentum distribution, and provide an intuitive physical picture. A discussion of various measures of the momentum correlations is also presented.

cond-mat.quant-gas↗
arXiv2021

Riemann zeros from a periodically-driven trapped ion

The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of physicists working in Random Matrix Theory and Quantum Chaos for decades. Here we present an experimental observation of the lowest non-trivial Riemann zeros by using a trapped ion qubit in a Paul trap, periodically driven with microwave fields. The waveform of the driving is engineered such that the dynamics of the ion is frozen when the driving parameters coincide with a zero of the real component of the zeta function. Scanning over the driving amplitude thus enables the locations of the Riemann zeros to be measured experimentally to a high degree of accuracy, providing a physical embodiment of these fascinating mathematical objects in the quantum realm.

quant-ph↗
arXiv2019

Identifying the Riemann zeros by periodically driving a single qubit

The Riemann hypothesis, one of the most important open problems in pure mathematics, implies the most profound secret of prime numbers. One of the most interesting approaches to solve this hypothesis is to connect the problem with the spectrum of the physical Hamiltonian of a quantum system. However, none of the proposed quantum Hamiltonians have been experimentally feasible.Here, we report the first experiment to identify the first non-trivial zeros of the Riemann zeta function and the first two zeros of Pólya's fake zeta function, using a novel Floquet method, through properly designed periodically driving functions. According to this method, the zeros of these functions are characterized by the occurrence of crossings of quasi-energies when the dynamics of the system are frozen. The experimentally obtained zeros are in excellent agreement with their exact values. Our study provides the first experimental realization of the Riemann zeros, which may provide new insights into this fundamental mathematical problem.

quant-ph↗
arXiv2019

Protected cat states from kinetic driving of a boson gas

We investigate the behavior of a one-dimensional Bose-Hubbard gas in both a ring and a hard-wall box, whose kinetic energy is made to oscillate with zero time-average, which suppresses first-order particle hopping. For intermediate and large driving amplitudes the system in the ring has similarities to the Richardson model, but with a peculiar type of pairing and an attractive interaction in momentum space. This analogy permits an understanding of some key features of the interacting boson problem. The ground state is a macroscopic quantum superposition, or cat state, of two many-body states collectively occupying opposite momentum eigenstates. Interactions give rise to a reduction (or modified depletion) cloud that is common to both macroscopically distinct states. Symmetry arguments permit a precise identification of the two orthonormal macroscopic many-body branches which combine to yield the ground state. In the ring, the system is sensitive to variations of the effective flux but in such a way that the macroscopic superposition is preserved. We discuss other physical aspects that contribute to protect the cat-like nature of the ground state.

cond-mat.quant-gas↗
arXiv2018

Relativistic motion of an Airy wavepacket in a lattice potential

We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its velocity, and so the acceleration cannot continue indefinitely. Instead, we show that the wavepacket's motion is described by relativistic equations of motion, which surprisingly, arise naturally from evolution under the standard non-relativistic Schrödinger equation. The presence of the lattice potential allows the wavepacket's motion to be controlled by means of Floquet engineering. In particular, in the deep relativistic limit when the wavepacket's motion is photon-like, this form of control allows it to mimic both standard and negative refraction. Airy wavepackets held in lattice potentials can thus be used as powerful and flexible simulators of relativistic quantum systems.

quant-ph↗
arXiv2016

Realization of uniform synthetic magnetic fields by periodically shaking an optical square lattice

Shaking a lattice system, by modulating the location of its sites periodically in time, is a powerful method to create effective magnetic fields in engineered quantum systems, such as cold gases trapped in optical lattices. However, such schemes are typically associated with space-dependent effective masses (tunneling amplitudes) and non-uniform flux patterns. In this work we investigate this phenomenon theoretically, by computing the effective Hamiltonians and quasienergy spectra associated with several kinds of lattice-shaking protocols. A detailed comparison with a method based on moving lattices, which are added on top of a main static optical lattice, is provided. This study allows the identification of novel shaking schemes, which simultaneously provide uniform effective mass and magnetic flux, with direct implications for cold-atom experiments and photonics.

cond-mat.quant-gas↗
arXiv2016

Long-range doublon transfer in a dimer chain induced by topology and ac fields

The controlled transfer of particles from one site of a spatial lattice to another is essential for many tasks in quantum information processing and quantum communication. Arrays of semiconductor quantum dots and ultracold atoms held in optical lattices, provide two means of studying coherent quantum transport in well-controlled systems. In this work we study how to induce long-range transfer between the two ends of a dimer chain, by coupling states that are localized just on the chain's end-points. This has the appealing feature that the transfer occurs only between the end-points -- the particle does not pass through the intermediate sites -- making the transfer less susceptible to decoherence. We first show how a repulsively bound-pair of fermions, known as a doublon, can be transferred from one end of the chain to the other via topological edge states. We then show how non-topological surface states of the familiar Shockley or Tamm type can be used to produce a similar form of transfer under the action of a periodic driving potential. Finally we show that combining these effects can produce transfer by means of more exotic topological effects, in which the driving field can be used to switch the topological character of the edge states, as measured by the Zak phase. Our results demonstrate how to induce long range transfer of strongly correlated particles by tuning both topology and driving.

cond-mat.quant-gas↗
arXiv2015

Finding zeros of the Riemann zeta function by periodic driving of cold atoms

The Riemann hypothesis, which states that the non-trivial zeros of the Riemann zeta function all lie on a certain line in the complex plane, is one of the most important unresolved problems in mathematics. Inspired by the Pólya-Hilbert conjecture, we propose a new approach to finding a physical system to study the Riemann zeros, which in contrast to previous examples, is based on applying a time-periodic driving field. This driving allows us to mould the quasienergies of the system (the analogue of the eigenenergies in the absence of driving), so that they are directly governed by the zeta function. We further show by numerical simulations that this allows the Riemann zeros to be measured in currently accessible cold atom experiments.

cond-mat.quant-gas↗
arXiv2014

Generation of uniform synthetic magnetic fields by split driving of an optical lattice

We describe a method to generate a synthetic gauge potential for ultracold atoms held in an optical lattice. Our approach uses a time-periodic driving potential based on two quickly alternating signals to engineer the appropriate Aharonov-Bohm phases, and permits the simulation of a uniform tunable magnetic field. We explicitly demonstrate that our split driving scheme reproduces the behavior of a charged quantum particle in a magnetic field over the complete range of field strengths, and obtain the Hofstadter butterfly band-structure for the Floquet quasienergies at high fluxes.

cond-mat.quant-gas↗
arXiv2014

Quantum simulation of correlated-hopping models with fermions in optical lattices

By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ from the Hubbard model in exhibiting additional density-dependent interaction terms that affect the hopping processes. In addition to the spin-SU(2) symmetry, they also possess a charge-SU(2) symmetry, which opens the possibility of investigating the $η$-pairing mechanism for superconductivity introduced by Yang for the Hubbard model. We discuss the known solution of the model in 1D (where $η$ states have been found in the degenerate manifold of the ground state) and show that, away from the integrable point, quantum Monte Carlo simulations at half filling predict the emergence of a phase with coexisting incommensurate spin and charge order.

cond-mat.quant-gas↗
arXiv2012

Orbital Josephson effect and interactions in driven atom condensates on a ring

In a system of ac-driven condensed bosons we study a new type of Josephson effect occurring between states sharing the same region of space and the same internal atom structure. We first develop a technique to calculate the long time dynamics of a driven interacting many-body system. For resonant frequencies, this dynamics can be shown to derive from an effective time-independent Hamiltonian which is expressed in terms of standard creation and annihilation operators. Within the subspace of resonant states, and if the undriven states are plane waves, a locally repulsive interaction between bosons translates into an effective attraction. We apply the method to study the effect of interactions on the coherent ratchet current of an asymmetrically driven boson system. We find a wealth of dynamical regimes which includes Rabi oscillations, self-trapping, and chaotic behavior. In the latter case, a full many-body calculation deviates from the mean-field results by predicting large quantum fluctuations of the relative particle number.

cond-mat.quant-gas↗
arXiv2011

Directed transport in driven optical lattices by phase generation

We examine the dynamics of ultracold atoms held in optical lattice potentials. By controlling the switching of a periodic driving potential we show how a phase-induced renormalization of the intersite tunneling can be used to produce directed motion and control wavepacket spreading. We further show how this generation of a synthetic gauge potential can be used to split and recombine wavepackets, providing an attractive route to implementing quantum computing tasks.

cond-mat.quant-gas↗
arXiv2010

Expansion of matter waves in static and driven periodic potentials

We study the non-equilibrium dynamics of cold atoms held in an optical lattice potential. The expansion of an initially confined atom cloud occurs in two phases: an initial quadratic expansion followed by a ballistic behaviour at long times. Accounting for this gives a good description of recent experimental results, and provides a robust method to extract the effective intersite tunneling from time-of-flight measurements.

cond-mat.quant-gas↗
arXiv2010

Reply to the Comment by Benenti et al

Benenti et al. recently submitted a Comment (arXiv:0912.3667) on our work "Coherent Ratchets in Driven Bose-Einstein condensates". We show that the main claim of the Comment is wrong, and correct some other misunderstandings presented there.

cond-mat.quant-gas↗
arXiv2010

Coherent control of interacting particles using dynamical and Aharonov-Bohm phases

A powerful method of manipulating the dynamics of quantum coherent particles is to control the phase of their tunneling. We consider a system of two electrons hopping on a quasi one-dimensional lattice in the presence of a uniform magnetic field, and study the effect of adding a time-periodic driving potential. We show that the dynamical phases produced by the driving can combine with the Aharonov-Bohm phases to give precise control of the localization and dynamics of the particles, even in the presence of strong particle interactions.

cond-mat.mes-hall↗
arXiv2009

Coherent ratchets in driven Bose-Einstein condensates

We study the response of a Bose-Einstein condensate to an unbiased periodic driving potential. By controlling the space and time symmetries of the driving we show how a directed current can be induced, producing a coherent quantum ratchet. Weak driving induces a regular behavior that is strongly governed by the interparticle interaction. Breaking both space and time symmetries is required to produce current flow. For strong driving the behavior becomes chaotic. The resulting effective irreversibility renders the space asymmetry sufficient to produce the ratchet effect, although the system is completely coherent.

cond-mat.quant-gas↗
arXiv2008

Instability and control of a periodically-driven Bose-Einstein condensate

We investigate the dynamics of a Bose-Einstein condensate held in an optical lattice under the influence of a strong periodic driving potential. Studying the mean-field version of the Bose-Hubbard model reveals that the condensate becomes highly unstable when the effective intersite tunneling becomes negative. We further show how controlling the sign of the tunneling can be used as a powerful tool to manage the dispersion of an atomic wavepacket, and thus to create a pulsed atomic soliton laser.

cond-mat.other↗