Rydberg Platform for Nonergodic Chiral Quantum Dynamics.

We propose a mechanism for engineering chiral interactions in Rydberg atoms via a directional antiblockade condition, where an atom can change its state only if an atom to its right (or left) is excited. The scalability of our scheme enables us to explore the many-body dynamics of kinetically constrained models with unidirectional character. We observe nonergodic behavior via either scars, confinement, or localization, upon simply tuning the strength of two driving fields acting on the atoms. We discuss how our mechanism persists in the presence of classical noise and how the degree of chirality in the interactions can be tuned, opening towards the frontier of directional, strongly correlated, quantum mechanics using neutral atoms arrays.

Observation of a Topological Edge State Stabilized by Dissipation.

Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to suitably modulated losses. Here, we study the dissipation-induced emergence of a topological band structure in a non-Hermitian one-dimensional lattice system, realized by arrays of plasmonic waveguides with tailored loss. We obtain direct evidence for a topological edge state that resides in the center of the band gap. By tuning dissipation and hopping, the formation and breakdown of an interface state between topologically distinct regions is demonstrated.

Ultracold Bose Gases in Dynamic Disorder with Tunable Correlation Time.

We study experimentally the dissipative dynamics of ultracold bosonic gases in a dynamic disorder potential with tunable correlation time. First, we measure the heating rate of thermal clouds exposed to the dynamic potential and present a model of the heating process, revealing the microscopic origin of dissipation from a thermal, trapped cloud of bosons. Second, for Bose-Einstein condensates, we measure the particle loss rate induced by the dynamic environment. Depending on the correlation time, the losses are either dominated by heating of residual thermal particles or the creation of excitations in the superfluid, a notion we substantiate with a rate model. Our results illuminate the interplay between superfluidity and time-dependent disorder and on more general grounds establish ultracold atoms as a platform for studying spatiotemporal noise and time-dependent disorder.

Finite-Temperature Topological Invariant for Interacting Systems.

We generalize the ensemble geometric phase, recently introduced to classify the topology of density matrices, to finite-temperature states of interacting systems in one spatial dimension (1D). This includes cases where the gapped ground state has a fractional filling and is degenerate. At zero temperature the corresponding topological invariant agrees with the well-known invariant of Niu, Thouless, and Wu. We show that its value at finite temperatures is identical to that of the ground state below some critical temperature T_{c} larger than the many-body gap. We illustrate our result with numerical simulations of the 1D extended superlattice Bose-Hubbard model at quarter filling. Here, a cyclic change of parameters in the ground state leads to a topological charge pump with fractional winding ν=1/2. The particle transport is no longer quantized when the temperature becomes comparable to the many-body gap, yet the winding of the generalized ensemble geometric phase is.

Evidence for Unbounded Growth of the Number Entropy in Many-Body Localized Phases.

We investigate the number entropy S_{N}-which characterizes particle-number fluctuations between subsystems-following a quench in one-dimensional interacting many-body systems with potential disorder. We find evidence that in the regime which is expected to show many-body localization and where the entanglement entropy grows as S∼lnt as function of time t, the number entropy grows as S_{N}∼lnlnt, indicating continuing subdiffusive particle transport at a very slow rate. We demonstrate that this growth is consistent with a relation between entanglement and number entropy recently established for noninteracting systems.

Dynamical Variational Approach to Bose Polarons at Finite Temperatures.

We discuss the interaction of a mobile quantum impurity with a Bose-Einstein condensate of atoms at finite temperature. To describe the resulting Bose polaron formation we develop a dynamical variational approach applicable to an initial thermal gas of Bogoliubov phonons. We study the polaron formation after switching on the interaction, e.g., by a radio-frequency (rf) pulse from a noninteracting to an interacting state. To treat also the strongly interacting regime, interaction terms beyond the Fröhlich model are taken into account. We calculate the real-time impurity Green's function and discuss its temperature dependence. Furthermore we determine the rf absorption spectrum and find good agreement with recent experimental observations. We predict temperature-induced shifts and a substantial broadening of spectral lines. The analysis of the real-time Green's function reveals a crossover to a linear temperature dependence of the thermal decay rate of Bose polarons as unitary interactions are approached.

Tunable Polarons of Slow-Light Polaritons in a Two-Dimensional Bose-Einstein Condensate.

When an impurity interacts with a bath of phonons it forms a polaron. For increasing interaction strengths the mass of the polaron increases and it can become self-trapped. For impurity atoms inside an atomic Bose-Einstein condensate (BEC) the nature of this transition is not understood. While Feynman's variational approach to the Fröhlich model predicts a sharp transition for light impurities, renormalization group studies always predict an extended intermediate-coupling region characterized by large phonon correlations. To investigate this intricate regime and to test polaron physics beyond the validity of the Fröhlich model we suggest a versatile experimental setup that allows us to tune both the mass of the impurity and its interactions with the BEC. The impurity is realized as a dark-state polariton (DSP) inside a quasi-two-dimensional BEC. We show that its interactions with the Bogoliubov phonons lead to photonic polarons, described by the Bogoliubov-Fröhlich Hamiltonian, and make theoretical predictions using an extension of a recently introduced renormalization group approach to Fröhlich polarons.

Topological growing of Laughlin states in synthetic gauge fields.

We suggest a scheme for the preparation of highly correlated Laughlin states in the presence of synthetic gauge fields, realizing an analogue of the fractional quantum Hall effect in photonic or atomic systems of interacting bosons. It is based on the idea of growing such states by adding weakly interacting composite fermions along with magnetic flux quanta one by one. The topologically protected Thouless pump ("Laughlin's argument") is used to create two localized flux quanta and the resulting hole excitation is subsequently filled by a single boson, which, together with one of the flux quanta, forms a composite fermion. Using our protocol, filling 1/2 Laughlin states can be grown with particle number N increasing linearly in time and strongly suppressed number fluctuations. To demonstrate the feasibility of our scheme, we consider two-dimensional lattices subject to effective magnetic fields and strong on-site interactions. We present numerical simulations of small lattice systems and also discuss the influence of losses.

Interfacing superconducting qubits and telecom photons via a rare-earth-doped crystal.

We propose a scheme to couple short single photon pulses to superconducting qubits. An optical photon is first absorbed into an inhomogeneously broadened rare-earth doped crystal using controlled reversible inhomogeneous broadening. The optical excitation is then mapped into a spin state using a series of π pulses and subsequently transferred to a superconducting qubit via a microwave cavity. To overcome the intrinsic and engineered inhomogeneous broadening of the optical and spin transitions in rare-earth doped crystals, we make use of a special transfer protocol using staggered π pulses. We predict total transfer efficiencies on the order of 90%.

Wigner crystallization of single photons in cold Rydberg ensembles.

The coupling of weak light fields to Rydberg states of atoms under conditions of electromagnetically induced transparency leads to the formation of Rydberg polaritons which are quasiparticles with tunable effective mass and nonlocal interactions. Confined to one spatial dimension their low energy physics is that of a moving-frame Luttinger liquid which, due to the nonlocal character of the repulsive interaction, can form a Wigner crystal of individual photons. We calculate the Luttinger K parameter using density-matrix renormalization group simulations and find that under typical slow-light conditions kinetic energy contributions are too strong for crystal formation. However, adiabatically increasing the polariton mass by turning a light pulse into stationary spin excitations allows us to generate true crystalline order over a finite length. The dynamics of this process and asymptotic correlations are analyzed in terms of a time-dependent Luttinger theory.

Topological edge States in the one-dimensional superlattice Bose-Hubbard model.

We analyze interacting ultracold bosonic atoms in a one-dimensional superlattice potential with alternating tunneling rates t1 and t2 and inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger model. A Z2 topological order parameter is introduced which is quantized for the Mott insulating (MI) phases. Depending on the ratio t1/t2 the n=1/2 MI phase is topologically nontrivial, which results in many-body edge states at open boundaries. In contrast to the Su-Schrieffer-Heeger model the bosonic counterpart lacks chiral symmetry and the edge states are no longer midgap. This leads to a generalization of the bulk-edge correspondence, which we discuss in detail. The edge states can be observed in cold atom experiments by creating a step in the effective confining potential, e.g., by a second heavy atom species, which leads to an interface between two MI regions with filling n=1 and n=1/2. The shape and energy of the edge states as well as the conditions for their occupation are determined analytically in the strong coupling limit and in general by density-matrix renormalization group simulations.

Electromagnetically induced transparency with Rydberg atoms.

We present a theory of electromagnetically induced transparency in a cold ensemble of strongly interacting Rydberg atoms. Long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our model is computationally very efficient and is in quantitative agreement with the results of the recent experiment of Pritchard et al. [Phys. Rev. Lett. 105, 193603 (2010)].

Photon-photon interactions via Rydberg blockade.

We develop the theory of light propagation under the conditions of electromagnetically induced transparency in systems involving strongly interacting Rydberg states. Taking into account the quantum nature and the spatial propagation of light, we analyze interactions involving few-photon pulses. We show that this system can be used for the generation of nonclassical states of light including trains of single photons with an avoided volume between them, for implementing photon-photon gates, as well as for studying many-body phenomena with strongly correlated photons.

Dynamical simulation of integrable and nonintegrable models in the Heisenberg picture.

The numerical simulation of quantum many-body dynamics is typically limited by the linear growth of entanglement with time. Recently numerical studies have shown that for 1D Bethe-integrable models the simulation of local operators in the Heisenberg picture can be efficient. Using the spin-1/2 XX chain as generic example of an integrable model that can be mapped to free fermions, we provide a simple explanation for this. We show furthermore that the same reduction of complexity applies to operators that have a high-temperature autocorrelation function which decays slower than exponential, i.e., with a power law. Thus efficient simulability may already be implied by a single conservation law as we will illustrate numerically for the spin-1 XXZ model.

Photon-number selective group delay in cavity induced transparency.

We show that the group velocity of a probe pulse in an ensemble of Λ-type atoms driven by a quantized cavity mode depends on the quantum state-of-the input probe pulse. In the strong-coupling regime of the atom-cavity system the probe group delay is photon-number selective. This can be used to spatially separate the single photon from higher photon-number components of a few-photon probe pulse and thus create a deterministic single-photon source.

Photonic phase gate via an exchange of fermionic spin waves in a spin chain.

We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the π phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed.

Dynamics of pair correlations in the attractive Lieb-Liniger gas.

We investigate the dynamics of a one-dimensional Bose gas after a quench from the Tonks-Girardeau regime to the regime of strong attractive interactions applying analytical techniques and numerical simulations. After the quench the system is found to be predominantly in an excited gaslike state, the so-called super-Tonks gas, however with a small coherent admixture of two-particle bound states. Despite its small amplitude, the latter leads to a pronounced oscillation of the local density correlation with a frequency corresponding to the binding energy of the pair. Contributions from bound states with larger particle numbers are found to be negligible.

Irreversible photon transfer in an ensemble of Lambda-type atoms and a photon diode.

We show that a pair of quantized modes interacting with a spectrally broadened ensemble of Lambda-type atoms is analogous to an ensemble of two-level systems coupled to a bosonic reservoir. This enables an irreversible photon transfer between photon modes. The reservoir can be engineered which allows the observation of effects such as the Zeno and anti-Zeno effect, the destructive interference of decay channels, and the decay in a squeezed vacuum. We also consider a photon diode, i.e., a device which directs a single photon from any one of two input ports to a common output port.

Frequency matching in light-storage spectroscopy of atomic Raman transitions.

We investigate the storage of light in an atomic sample with a Lambda-type coupling scheme driven by optical fields at variable two-photon detuning. In the presence of electromagnetically induced transparency (EIT), light is stored and retrieved from the sample by dynamically varying the group velocity. It is found that for any two-photon detuning of the input light pulse within the EIT transparency window, the carrier frequency of the retrieved light pulse matches the two-photon resonance frequency with the atomic ground state transition and the control field. This effect which is not based on spectral filtering is investigated both theoretically and experimentally. It can be used for high-speed precision measurements of the two-photon resonance as employed, e.g., in optical magnetometry.