Jiří Minář

Topological properties of a dense atomic lattice gas.

We investigate the existence of topological phases in a dense two-dimensional atomic lattice gas. The coupling of the atoms to the radiation field gives rise to dissipation and a non-trivial coherent long-range exchange interaction whose form goes beyond a simple power-law. The far-field terms of the potential -- which are particularly relevant for atomic separations comparable to the atomic transition wavelength -- can give rise to energy spectra with one-sided divergences in the Brillouin zone. The long-ranged character of the interactions has another important consequence: it can break the standard bulk-boundary relation in topological insulators. We show that topological properties such as the transport of an excitation along the edge of the lattice are robust with respect to the presence of lattice defects and dissipation. The latter is of particular relevance as dissipation and coherent interactions are inevitably connected in our setting.

Facilitation Dynamics and Localization Phenomena in Rydberg Lattice Gases with Position Disorder

We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.Disordered systems provide paradigmatic instances of ergodicity breaking and localization phenomena. Here we explore the dynamics of excitations in a system of Rydberg atoms held in optical tweezers. The finite temperature produces an intrinsic uncertainty in the atomic positions, which translates into quenched correlated disorder in the interatomic interaction strengths. In a simple approach, the dynamics in the many-body Hilbert space can be understood in terms of a one-dimensional Anderson-like model with disorder on every other site, featuring both localized and delocalized states. We conduct an experiment on an eight-atom chain and observe a clear suppression of excitation transfer. Our experiment accesses a regime which is described by a twodimensional Anderson model on a “trimmed” square lattice. Our results thus provide a concrete example in which the absence of excitation propagation in a many-body system is directly related to Anderson-like localization in the Hilbert space, which is believed to be the mechanism underlying many-body localization.

Crystalline structures and frustration in a two-component Rydberg gas

We study the static behavior of a gas of atoms held in a one-dimensional lattice where two distinct electronically high-lying Rydberg states are simultaneously excited by laser light. We focus on a situation where interactions of van-der-Waals type take place only among atoms that are in the same Rydberg state. We analytically investigate at first the so-called classical limit of vanishing laser driving strength. We show that the system exhibits a surprisingly complex ground state structure with a sequence of compatible to incompatible transitions. The incompatibility between the species leads to mutual frustration, a feature which pertains also in the quantum regime. We perform an analytical and numerical investigation of these features and present an approximative description of the system in terms of a Rokhsar–Kivelson Hamiltonian which permits the analytical understanding of the frustration effects even beyond the classical limit.

Quantum memory with a single two-level atom in a half cavity

We propose a setup for quantum memory based on a single two-level atom in a half cavity with a moving mirror. We show that various temporal shapes of incident photon can be efficiently stored and readout by shaping the time-dependent decay rate

Emergent devil's staircase without particle-hole symmetry in Rydberg quantum gases with competing attractive and repulsive interactions

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State-dependent atomic excitation by multiphoton pulses propagating along two spatial modes

between the atom and the light. This is achieved uniquely by an appropriate motion of the mirror without the need for additional control laser or atomic level. We present an analytical expression for the efficiency of the process and study its dependence on the ratio between the incident light field bandwidth and the atomic decay rate. We discuss possible implementations and experimental issues, particularly for a single atom or ion in a half cavity quantum optical setup as well as a superconducting qubit in the context of circuit QED.

Electric control of collective atomic coherence in an erbium-doped solid

The devils staircase is a fractal structure that characterizes the ground state of one-dimensional classical lattice gases with long-range repulsive convex interactions. Its plateaus mark regions of stability for specific filling fractions which are controlled by a chemical potential. Typically, such a staircase has an explicit particle-hole symmetry; i.e., the staircase at more than half filling can be trivially extracted from the one at less than half filling by exchanging the roles of holes and particles. Here, we introduce a quantum spin chain with competing short-range attractive and long-range repulsive interactions, i.e., a nonconvex potential. In the classical limit the ground state features generalized Wigner crystals that--depending on the filling fraction--are composed of either dimer particles or dimer holes, which results in an emergent complete devils staircase without explicit particle-hole symmetry of the underlying microscopic model. In our system the particle-hole symmetry is lifted due to the fact that the staircase is controlled through a two-body interaction rather than a one-body chemical potential. The introduction of quantum fluctuations through a transverse field melts the staircase and ultimately makes the system enter a paramagnetic phase. For intermediate transverse field strengths, however, we identify a region where the density-density correlations suggest the emergence of quasi-long-range order. We discuss how this physics can be explored with Rydberg-dressed atoms held in a lattice.

Crystalline structures in a one-dimensional two-component lattice gas with 1/r α interactions

We investigate the dynamics of a single two-level atom, which interacts with pulses propagating in two spatial-modes (right and left) and frequency-continuum. Using Heisenberg equations of motion, we present the explicit analytical derivations and general formalisms for atomic excitation with two spatial-mode multi-photon pulses in both Fock state and coherent state. Based on those formalisms, we show that perfect atomic excitation by single photon Fock state pulse can only be realized when it is rising-exponentially shaped in the even-mode---a balanced superposition of the two spatial-modes. Single photon from single spatial-mode can only give half of the maximal atomic excitation probability. We also show that the maximum atomic excitation probability with multi-photon pulses in the even-mode is a monotonic function of the average photon number for coherent state, but not for Fock states. Furthermore, we demonstrate that the atomic dynamics can be controlled by the relative phase between the two counter-propagating coherent state pulses incident on the atom, which is not the case with two Fock state pulses.

Effective spin physics in two-dimensional cavity QED arrays

We demonstrate the fast and accurate control of the evolution of collective atomic coherences in an erbium-doped solid using external electric fields. This is achieved by controlling the inhomogeneous broadening of erbium ions emitting at 1536 nm using an electric field gradient, thanks to the linear Stark effect. The manipulation of atomic coherence is characterized with the collective spontaneous emission (optical free induction decay (FID)) emitted by the sample after an optical excitation, which does not require any previous preparation of the atoms. We show that controlled dephasing and rephasing of the atoms by the electric field result in collapses and revivals of the optical FID. Our results show that the use of external electric fields does not introduce any substantial decoherence and enables the manipulation of collective atomic coherence with a very high degree of precision on the timescale of tens of nanoseconds. This provides an interesting resource for photonic quantum state storage and quantum state manipulation.

Prospects of charged-oscillator quantum-state generation with Rydberg atoms

We investigate the ground state of a one-dimensional lattice system that hosts two different kinds of excitations (species) which interact with a power-law potential. Interactions are only present between excitations of the same kind and the interaction strength can be species-dependent. For the case in which only one excitation is permitted per site we derive a prescription for determining the ground state configuration as a function of the filling fractions of the two species. We show that depending on the filling fractions compatible or incompatible phases emerge. Furthermore, we discuss in detail the case in which one species is strongly and the other one weakly interacting. In this case the configuration of the strongly interacting (strong) species can be considered frozen and forms an effective inhomogeneous lattice for the other (weak) species. In this limit we work out in detail the microscopic ground state configuration and show that by varying the density of the weak species a series of compatible–incompatible transitions occurs. Finally, we determine the stability regions of the weak species in the compatible phase and compare it with numerical simulations.