We study the three-body problem of two ultracold identical bosonic atoms (denoted by $B$) and one extra atom (denoted by $X$), where the scattering length $a_{BX}$ between each bosonic atom and atom $X$ is resonantly large and positive. We calculate the scattering length $a_{\mathrm{ad}}$ between one bosonic atom and the shallow dimer formed by the other bosonic atom and atom $X$, and investigate the effect induced by the interaction between the two bosonic atoms. We find that even if this interaction is weak (i.e., the corresponding scattering length $a_{BB}$ is of the same order of the van der Waals length $r_{\mathrm{vdW}}$ or even smaller), it can still induce a significant effect for the atom-dimer scattering length $a_{\mathrm{ad}}$. Explicitly, an atom-dimer scattering resonance can always occur when the value of $a_{BB}$ varies in the region with $|a_{BB}|\lesssim r_{\mathrm{vdW}}$. As a result, both the sign and the absolute value of $a_{\mathrm{ad}}$, as well as the behavior of the $a_{\mathrm{ad}}\text{−}{a}_{BX}$ function, depends sensitively on the exact value of $a_{BB}$. Our results show that, for a good quantitative theory, the intraspecies interaction is required to be taken into account for this heteronuclear system, even if this interaction is weak.

We report a systematic experimental and numerical study of the expansion of ultracold Rydberg plasmas. Specifically, we have measured the asymptotic expansion velocities, $v_0$, of ultracold neutral plasmas (UNPs) which evolve from cold, dense samples of Rydberg rubidium atoms using ion time-of-flight spectroscopy. From this, we have obtained values for the effective initial plasma electron temperature, $T_{e,0}=m_{\mathrm{ion}}{v}_0^2/k_B$ (where $m_{\mathrm{ion}}$ is the ${\mathrm{Rb}}^{+}$ ion mass), as a function of the original Rydberg atom density and binding energy, $E_{b,i}$. We have also simulated numerically the interaction of UNPs with a large reservoir of Rydberg atoms to obtain data to compare with our experimental results. We find that for Rydberg atom densities in the range ${10}^7–{10}^9 {\mathrm{cm}}^{-3}$, for states with principal quantum number $n>40, T_{e,0}$ is insensitive to the initial ionization mechanism which seeds the plasma. In addition, the quantity $k_B{T}_{e,0}$ is strongly correlated with the fraction of atoms which ionize, and is in the range $0.6\times |E_{b,i}|\lesssim k_B{T}_{e,0}\lesssim 2.5\times \left|E_{b,i}\right|$. On the other hand, plasmas from Rydberg samples with $n\lesssim 40$ evolve with no significant additional ionization of the remaining atoms once a threshold number of ions has been established. The dominant interaction between the plasma electrons and the Rydberg atoms is one in which the atoms are deexcited, a heating process for electrons that competes with adiabatic cooling to establish an equilibrium where $T_{e,0}$ is determined by their Coulomb coupling parameter, ${\mathrm{\Gamma }}_e\sim 0.01$.

We explore the quantum many-body physics of a driven Bose-Einstein condensate in optical lattices. The laser field induces a gap in the generalized Bogoliubov spectrum proportional to the effective Rabi frequency. The lowest-lying modes in a driven condensate are characterized by zero group velocity and nonzero current. Thus, the laser field induces roton modes, which carry interaction in a driven condensate. We show that collective excitations below the energy of the laser-induced gap remain undamped, while above the gap they are characterized by a significantly suppressed Landau damping rate.

Progress in high-harmonic generation has led to high-energy attosecond pulses with cutoff above the carbon $1s$ edge (283.8 eV). These pulses are essential to extend time-resolved spectroscopies to the water window in order to control electron dynamics in solvated organic species. Here we report a step towards this goal: the measurement, with subcycle time resolution, of the attosecond transient absorption spectrum of argon at the $2p^{-1} L_{2,3}$ edge ($\sim 250$ eV) in the presence of a short-wave infrared control pulse. The measurements, supported by theoretical simulations, demonstrate the concurrent role of Auger decay and tunnel ionization in the driven evolution of inner-valence holes of polyelectronic atoms.

Floquet systems provide a platform with significant potential for generating and controlling topological phases of matter. By introducing an external driving field, a topologically trivial system can be driven to topological phases possessing nonzero bulk invariants and associated gapless surface modes. One rich feature of Floquet systems is that, as one moves away from the weak-field regime by increasing the amplitude of the driving field, one can encounter a series of topological transitions which place the system in distinct topological phases. Here we experimentally demonstrate this phenomenon in a photonic system consisting of an array of evanescently coupled helical waveguides. We show that, by moving between the weakly and strongly driven regimes, we can induce a transition in which the bulk topological invariant changes sign and the associated topological edge mode reverses its propagation direction. These two topological phases are part of a larger phase diagram and serve to demonstrate both the rich topological physics present in Floquet systems as well as the accessibility of the strongly driven regime—a regime typically associated with the difficulties of large radiative losses for photonic systems and significant heating for their condensed matter counterparts.

The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian $\mathcal{PT}$-symmetric models.

Broadcasting information anonymously becomes more difficult as surveillance technology improves, but remarkably, quantum protocols exist that enable provably traceless broadcasting. The difficulty is making scalable entangled resource states that are robust to errors. We propose an anonymous broadcasting protocol that uses a continuous-variable surface-code state that can be produced using current technology. High squeezing enables large transmission bandwidth and strong anonymity, and the topological nature of the state enables local error mitigation.

The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat-binomial-GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multiqubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a multiqudit code.

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

The relationship between two-dimensional $\text{SO}(2,1)$ conformal anomalies in nonrelativistic systems and the virial expansion is explored using recently developed path-integral methods. In the process, the Beth-Uhlenbeck formula for the shift of the second virial coefficient $\delta b_2$ is obtained, as well as a virial expansion for the Tan contact. A possible extension of these techniques for higher orders in the virial expansion is discussed.

Probing the out-of-equilibrium dynamics of quantum matter has gained renewed interest owing to immense experimental progress in artificial quantum systems. Dynamical quantum measures such as the growth of entanglement entropy and out-of-time-ordered correlators (OTOCs) have been shown to provide great insight by exposing subtle quantum features invisible to traditional measures such as mass transport. However, measuring them in experiments requires either identical copies of the system, an ancilla qubit coupled to the whole system, or many measurements on a single copy, thereby making scalability extremely complex and hence, severely limiting their potential. Here, we introduce an alternative quantity, the out-of-time-ordered measurement (OTOM), which involves measuring a single observable on a single copy of the system, while retaining the distinctive features of the OTOCs. We show, theoretically, that OTOMs are closely related to OTOCs in a doubled system with the same quantum statistical properties as the original system. Using exact diagonalization, we numerically simulate classical mass transport, as well as quantum dynamics through computations of the OTOC, the OTOM, and the entanglement entropy in quantum spin chain models in various interesting regimes (including chaotic and many-body localized systems). Our results demonstrate that an OTOM can successfully reveal subtle aspects of quantum dynamics hidden to classical measures and, crucially, provide experimental access to them.

We examine the influence of probe-laser-intensity fluctuations on hyper-Ramsey spectroscopy. We assume, as is appropriate for relevant cases of interest, that the probe-laser intensity $I$ determines both the Rabi frequency ($\propto \sqrt{I}$) and the frequency shift to the atomic transition ($\propto I$) during probe-laser interactions with the atom. The spectroscopic signal depends on these two quantities that covary with fluctuations in the probe-laser intensity. Introducing a simple model for the fluctuations, we find that the signature robustness of the hyper-Ramsey method can be compromised. Taking the ${\mathrm{Yb}}^{+}$ electric octupole clock transition as an example, we quantify the clock error under different levels of probe-laser-intensity fluctuations.

We consider an ideal experiment in which unlimited nonprojective quantum measurements are sequentially performed on a system that is initially entangled with a distant one. At each step of the sequence, the measurements are randomly chosen between two. However, regardless of which measurement is chosen or which outcome is obtained, the quantum state of the pair always remains entangled. We show that the classical simulation of the reduced state of the distant system requires not only unlimited rounds of communication, but also that the distant system has infinite memory. Otherwise, a thermodynamical argument predicts heating at a distance. Our proposal can be used for experimentally ruling out nonlocal finite-memory classical models of quantum theory.

We analytically diagonalize a discrete-time on-site interacting fermionic cellular automaton in the two-particle sector. Important features of the solutions sensibly differ from those of analogous Hamiltonian models. In particular, we find a wider variety of scattering processes, we have bound states for every value of the total momentum, and there exist bound states also in the free case, where the coupling constant is null.

The exploitation and characterization of memory effects arising from the interaction between system and environment is a key prerequisite for quantum reservoir engineering beyond the standard Markovian limit. In this paper we investigate a prototype of non-Markovian dynamics experimentally implementable with superconducting qubits. We rigorously quantify non-Markovianity, highlighting the effects of the environmental temperature on the Markovian to non-Markovian crossover. We investigate how memory effects influence, and specifically suppress, the ability to perform work on the driven qubit. We show that the average work performed on the qubit can be used as a diagnostic tool to detect the presence or absence of memory effects.

The maximal-clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, and bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal-clique problem for any graph $G$ with $n$ vertices with quadratic speedup over its classical counterparts, where the time and spatial complexities are reduced to, respectively, $O\left(\sqrt{2^n}\right)$ and $O\left(n^2\right)$. With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed quantum algorithm, we successfully solve a typical clique problem for a graph $G$ with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.

A Rydberg interaction that can effectively exchange the states of two atoms may be used to transfer the optical phase of laser fields to the atomic pair wave function. A similar phase mapping may occur for many neutral atoms in a two-dimensional lattice when subjected to off-resonant optical Rydberg dressing fields, simulating the effect of a magnetic field. This all-optical method of simultaneously simulating magnetic fields and strong two-body interaction may have application to the study of quantum magnetism and topological physics.

A possible route to extract electronic and nuclear dynamics from molecular targets with attosecond temporal and nanometer spatial resolution is to employ recolliding electrons as “probes.” The recollision process in molecules is, however, very challenging to treat using ab initio approaches. Even for the simplest diatomic systems, such as ${\mathrm{H}}_2$, today's computational capabilities are not enough to give a complete description of the electron and nuclear dynamics initiated by a strong laser field. As a consequence, approximate qualitative descriptions are called to play an important role. In this paper we extend the work presented in Suárez et al. [N. Suárez, A. Chacón, J. A. Pérez-Hernández, J. Biegert, M. Lewenstein, and M. F. Ciappina, High-order-harmonic generation in atomic and molecular systems, Phys. Rev. A 95, 033415 (2017)] to three-center molecular targets. Additionally, we incorporate a more accurate description of the molecular ground state, employing information extracted from quantum chemistry software packages. This step forward allows us to include, in a detailed way, both the molecular symmetries and nodes present in the high-occupied molecular orbital. We are able, on the one hand, to keep our formulation as analytical as in the case of diatomics and, on the other hand, to still give a complete description of the underlying physics behind the above-threshold ionization process. The application of our approach to complex multicenter—with more than three centers—targets appears to be straightforward.

We study the effects of quantum and thermal fluctuations on Bose-Bose mixtures at finite temperature employing the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The theory governs self-consistently the motion of the condensates, the noncondensates, and of the anomalous components on an equal footing. The finite temperature criterion for the phase separation is established. We numerically analyze the temperature dependence of different densities for both miscible and immiscible mixtures. We show that the degree of the overlap between the two condensates and the thermal clouds is lowered and the relative motion of the centers of mass of the condensed and thermal components is strongly damped due to the presence of the pair anomalous fluctuations. Our results are compared with previous theoretical and experimental findings. On the other hand, starting from our TDHFB equations, we develop a random-phase theory for the elementary excitations in a homogeneous mixture. We find that the normal and anomalous fluctuations may lead to enhance the excitations and the thermodynamics of the system.

Experimental realizations of a variety of atomic binary Bose-Fermi mixtures have brought opportunities for studying composite quantum systems with different spin statistics. The binary atomic mixtures can exhibit a structural transition from a mixture into phase separation as the boson-fermion interaction increases. By using a path-integral formalism to evaluate the grand partition function and the thermodynamic grand potential, we obtain the effective potential of binary Bose-Fermi mixtures. Thermodynamic quantities in a broad range of temperatures and interactions are also derived. The structural transition can be identified as a loop of the effective potential curve, and the volume fraction of phase separation can be determined by the lever rule. For ${}^6\mathrm{Li}-{}^7\mathrm{Li}$ and ${}^6\mathrm{Li}-{}^{41}\mathrm{K}$ mixtures, we present the phase diagrams of the mixtures in a box potential at zero and finite temperatures. Due to the flexible densities of atomic gases, the construction of phase separation is more complicated when compared to conventional liquid or solid mixtures where the individual densities are fixed. For harmonically trapped mixtures, we use the local density approximation to map out the finite-temperature density profiles and present typical trap structures, including the mixture, partially separated phases, and fully separated phases.