Generation of photonic tensor network states with Circuit QED

We propose a circuit QED platform and protocol to deterministically generate microwave photonic tensor network states. We first show that using a microwave cavity as ancilla and a transmon qubit as emitter is a favorable platform to produce photonic matrix-product states. The ancilla cavity combines a large controllable Hilbert space with a long coherence time, which we predict translates into a high number of entangled photons and states with a high bond dimension. Going beyond this paradigm, we then consider a natural generalization of this platform, in which several cavity--qubit pairs are coupled to form a chain. The photonic states thus produced feature a two-dimensional entanglement structure and are readily interpreted as $textit{radial plaquette}$ projected entangled pair states, which include many paradigmatic states, such as the broad class of isometric tensor network states, graph states, string-net states.

Atomic waveguide QED with atomic dimers

Quantum emitters coupled to a waveguide is a paradigm of quantum optics, whose essential properties are described by waveguide quantum electrodynamics (QED). We study the possibility of observing the typical features of the conventional waveguide QED scenario in a system where the role of the waveguide is played by a one-dimensional subwavelength atomic array. For the role of emitters, we propose to use anti-symmetric states of atomic dimers - a pair of closely spaced atoms - as effective two-level systems, which significantly reduces the effect of free-space spontaneous emission. We solve the dynamics of the system both when the dimer frequency lies inside and when it lies outside the band of modes of the array. Along with well-known phenomena of collective emission into the guided modes and waveguide mediated long-range dimer-dimer interactions, we uncover significant non-Markovian corrections which arise from both the finiteness of the array and through retardation effects.

Convergence of numerical approximations to non-Markovian bosonic gaussian environments

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. A common approach to the analysis of such systems is to approximate the non-Markovian environment by discrete bosonic modes thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been proposed in previous works [D. Tamascelli et al, PRL (2012), A. W. Chin et al, J. of Math. Phys (2010)], the resulting approximation lacks rigorous convergence guarantees. In this paper, we initiate a rigorous study of the convergence properties of these methods. We show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that, for most physically interesting models of non-Markovian environments, the approximation error falls off polynomially with the number of modes. Our results lend rigor to numerical methods used for approximating non-Markovian quantum dynamics and allow for a quantitative assessment of classical as well as quantum algorithms in simulating non-Markovian quantum systems.

Sequential generation of projected entangled-pair states

We introduce plaquette projected entangled-pair states, a class of states in a lattice that can be generated by applying sequential unitaries acting on plaquettes of overlapping regions. They satisfy area-law entanglement, possess long-range correlations, and naturally generalize other relevant classes of tensor network states. We identify a subclass that can be more efficiently prepared in a radial fashion and that contains the family of isometric tensor network states. We also show how such subclass can be efficiently prepared using an array of photon sources.

Quantum simulation with fully coherent dipole--dipole-interactions mediated by three-dimensional subwavelength atomic arrays

Quantum simulators employing cold atoms are among the most promising approaches to tackle quantum many-body problems. Nanophotonic structures are widely employed to engineer the bandstructure of light and are thus investigated as a means to tune the interactions between atoms placed in their vicinity. A key shortcoming of this approach is that excitations can decay into free photons, limiting the coherence of such quantum simulators. Here, we overcome this challenge by proposing to use a simple cubic three-dimensional array of atoms to produce an omnidirectional bandgap for light and show that it enables coherent, dissipation-free interactions between embedded impurities. We show explicitly that the band gaps persist for moderate lattice sizes and finite filling fraction, which makes this effect readily observable in experiment. Our work paves the way toward analogue spin quantum simulators with long-range interactions using ultracold atomic lattices, and is an instance of the emerging field of atomic quantum metamaterials.

Topological two-dimensional Floquet lattice on a single superconducting qubit

Previous theoretical and experimental research has shown that current NISQ devices constitute powerful platforms for analogue quantum simulation. With the exquisite level of control offered by state-of-the-art quantum computers, we show that one can go further and implement a wide class of Floquet Hamiltonians, or timedependent Hamiltonians in general. We then implement a single-qubit version of these models in the IBM Quantum Experience and experimentally realize a temporal version of the Bernevig-Hughes-Zhang Chern insulator. From our data we can infer the presence of a topological transition, thus realizing an earlier proposal of topological frequency conversion by Martin, Refael, and Halperin. Our study highlights promises and limitations when studying many-body systems through multi-frequency driving of quantum computers.

Generation of Photonic Matrix Product States with Rydberg Atomic Arrays

We show how one can deterministically generate photonic matrix product states with high bond and physical dimensions with an atomic array if one has access to a Rydberg-blockade mechanism. We develop both a quantum gate and an optimal control approach to universally control the system and analyze the photon retrieval efficiency of atomic arrays. Comprehensive modeling of the system shows that our scheme is capable of generating a large number of entangled photons. We further develop a multi-port photon emission approach that can efficiently distribute entangled photons into free space in several directions, which can become a useful tool in future quantum networks.

To heat or not to heat: time crystallinity and finite-size effects in clean Floquet systems

A cornerstone assumption that most literature on discrete time crystals has relied on is that homogeneous Floquet systems generally heat to a featureless infinite temperature state, an expectation that motivated researchers in the field to mostly focus on many-body localized systems. Some works have however shown that the standard diagnostics for time crystallinity apply equally well to clean settings without disorder. This fact raises the question whether an homogeneous discrete time crystal is possible in which the originally expected heating is evaded. Studying both a localized and an homogeneous model with short-range interactions, we clarify this issue showing explicitly the key differences between the two cases. On the one hand, our careful scaling analysis confirms that, in the thermodynamic limit and in contrast to localized discrete time crystals, homogeneous systems indeed heat. On the other hand, we show that, thanks to a mechanism reminiscent of quantum scars, finite-size homogeneous systems can still exhibit very crisp signatures of time crystallinity. A subharmonic response can in fact persist over timescales that are much larger than those set by the integrability-breaking terms, with thermalization possibly occurring only at very large system sizes (e.g., of hundreds of spins). Beyond clarifying the emergence of heating in disorder-free systems, our work casts a spotlight on finite-size homogeneous systems as prime candidates for the experimental implementation of nontrivial out-of-equilibrium physics.

Optimal two-photon excitation of bound states in non-Markovian waveguide QED

Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave-packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave-packets that can excite a given superposition of these bound states. As specific examples, we study bound state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.

Seasonal epidemic spreading on small-world networks: Biennial outbreaks and classical discrete time crystals

We study seasonal epidemic spreading in a susceptible-infected-removed-susceptible (SIRS) model on smallworld graphs. We derive a mean-field description that accurately captures the salient features of the model, most notably a phase transition between annual and biennial outbreaks. A numerical scaling analysis exhibits a diverging autocorrelation time in the thermodynamic limit, which confirms the presence of a classical discrete time crystalline phase. We derive the phase diagram of the model both from mean-field theory and from numerics. Our work offers new perspectives by demonstrating that small-worldness and non-Markovianity can stabilize a classical discrete time crystal, and by linking recent efforts to understand such dynamical phases of matter to the century-old problem of biennial epidemics.