We propose a method to find asymptotic states of a class of periodically modulated open systems which are outside the range of validity of the Floquet theory due to the presence of memory effects. The method is based on a Floquet treatment of the time-local, memoryless dynamics taking place in a minimally enlarged state space where the original system is coupled to auxiliary—typically nonphysical—variables. A projection of the Floquet solution into the physical subspace returns the sought asymptotic state of the system. The spectral gap of the Floquet propagator acting in the enlarged state space can be used to estimate the relaxation time. We illustrate the method with a modulated quantum random walk model.

The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground-state subspace of a certain quantum optimization problem. This involves extending the notion of clustering to Hilbert space, where the classical Hamming distance is not immediately useful. Quantum clusters correspond to macroscopically distinct subspaces of the full quantum ground-state space which grow with the system size. We explicitly demonstrate that such clusters arise in the solution space of random quantum satisfiability (3-QSAT) at its satisfiability transition. We estimate both the number of these clusters and their internal entropy. The former are given by the number of hard-core dimer coverings of the core of the interaction graph, while the latter is related to the underconstrained degrees of freedom not touched by the dimers. We additionally provide numerical evidence suggesting that the 3-QSAT satisfiability transition may coincide with the product satisfiability transition, which would imply the absence of an intermediate entangled satisfiable phase.

In this work, we study a system of interacting fermions with large spin and SP($N$) symmetry. We contrast their behavior with the case of SU($N$) symmetry by analyzing the conserved quantities and the dynamics in each case. We also develop the Fermi liquid theory for fermions with SP($N$) symmetry. We find that the effective mass and inverse compressibility are always enhanced in the presence of interactions and that the $N$ dependence of the enhancement is qualitatively different in distinct parameter regimes. The Wilson ratio can be enhanced, indicating that the system can be made closer to a magnetic instability, in contrast to the SU($N$) scenario. We conclude by discussing the experimental routes to SP($N$) symmetry within cold atoms and the exciting possibility of realizing physics in higher dimensions in these systems.

We propose a low-noise, triply resonant, electro-optic (EO) scheme for quantum microwave-to-optical conversion based on coupled nanophotonics resonators integrated with a superconducting qubit. Our optical system features a split resonance—a doublet—with a tunable frequency splitting that matches the microwave resonance frequency of the superconducting qubit. This is in contrast to conventional approaches, where large optical resonators with free-spectral range comparable to the qubit microwave frequency are used. In our system, EO mixing between the optical pump coupled into the low-frequency doublet mode and a resonance microwave photon results in an up-converted optical photon on resonance with high-frequency doublet mode. Importantly, the down-conversion process, which is the source of noise, is suppressed in our scheme as the coupled-resonator system does not support modes at that frequency. Our device has at least an order of magnitude smaller footprint than conventional devices, resulting in large overlap between optical and microwave fields and a large photon conversion rate ($g/2\pi$) in the range of $\sim 5$–15 kHz. Owing to a large $g$ factor and doubly resonant nature of our device, microwave-to-optical frequency conversion can be achieved with optical pump powers in the range of tens of microwatts, even with moderate values for optical $\mathit{Q}$ ($\sim {10}^6$) and microwave $Q$ ($\sim {10}^4$). The performance metrics of our device, with substantial improvement over the previous EO-based approaches, promise a scalable quantum microwave-to-optical conversion and networking of superconducting processors via optical fiber communication.

We study the nonequilibrium steady state of the driven-dissipative Bose-Hubbard model with Kerr nonlinearity. Employing a mean-field decoupling for the intercavity hopping $J$, we find that the steep crossover between low and high photon-density states inherited from the single cavity transforms into a gas–liquid bistability at large cavity-coupling $J$. We formulate a van der Waals–like gas–liquid phenomenology for this nonequilibrium setting and determine the relevant phase diagrams, including a new type of diagram where a lobe-shaped boundary separates smooth crossovers from sharp, hysteretic transitions. Calculating quantum trajectories for a one-dimensional system, we provide insights into the microscopic origin of the bistability.

We study the effects of the position of the passive and active cavities on the spontaneous parity-time- ($\mathcal{PT}$-) symmetry-breaking behavior in a non-Hermitian coupled-cavity-array model. We analyze and discuss the energy eigenvalue spectra and $\mathcal{PT}$ symmetry in the topologically trivial and nontrivial regimes under three different cases in detail; that is, the passive and active cavities are located at, respectively, the two end positions, the second and penultimate positions, and each position in the coupled-cavity array. The odevity of the number of cavities is further considered to check the effects of the non-Hermitian terms applied on the $\mathcal{PT}$-symmetric and -asymmetric systems. We find that the position of the passive and active cavities has remarkable impacts on the spontaneous $\mathcal{PT}$-symmetry-breaking behavior, and in each case the system exhibits distinguishable and novel spontaneous $\mathcal{PT}$-symmetry-breaking characteristics. The effects of the non-Hermitian terms on the $\mathcal{PT}$-symmetric and -asymmetric systems due to the odevity are comparatively different in the first case but qualitatively the same in the second case.

The interaction of quantum emitters with structured baths modifies both their individual and collective dynamics. In A. González-Tudela and J. I. Cirac, Phys. Rev. Lett. 119, 143602 (2017), we show how exotic quantum dynamics emerges when quantum emitters are spectrally tuned around the middle of the band of a two-dimensional structured reservoir, where we predict the failure of perturbative treatments, anisotropic non-Markovian interactions, and remarkable superradiant and subradiant behavior. In this work, we provide further analysis of that situation, together with a complete analysis for the quantum emitter dynamics in spectral regions different from the center of the band.

We address memory effects and diffusive properties of a continuous-time quantum walk on a one-dimensional percolation lattice affected by spatially correlated random telegraph noise. In particular, by introducing spatially correlated time-dependent fluctuations in nearest-neighbor hopping amplitudes, we describe random domains characterized by global noise. The resulting open dynamics of the walker is then unraveled by an ensemble average over all the noise realizations. Our results show that time-dependent noise assisted by spatial correlations leads to strong memory effects in the walker dynamics and to robust diffusive behavior against the detrimental action of uncorrelated noise. We also show that spatially correlated classical noise enhances localization breaking, thus making a quantum particle spread on longer distances across the lattice.

Ambiguous measurements do not reveal complete information about the system under test. Their quantum-mechanical counterparts are semiweak (or in the limit, weak) measurements and here we discuss their role in tests of the Leggett-Garg inequalities. We show that, while ambiguous measurements allow one to forgo the usual noninvasive measurability assumption, to derive a Leggett-Garg inequality that may be violated, we are forced to introduce another assumption that equates the invasive influence of ambiguous and unambiguous detectors. Based on this assumption, we derive signaling conditions that should be fulfilled for the plausibility of the Leggett-Garg test. We then propose an experiment on a three-level system with a direct quantum-optics realization that satisfies all signaling constraints and violates a Leggett-Garg inequality.

A non-Clifford gate is required for universal quantum computation, and, typically, this is the most error-prone and resource-intensive logical operation on an error-correcting code. Small, single-qubit rotations are popular choices for this non-Clifford gate, but certain three-qubit gates, such as Toffoli or controlled-controlled-$Z$ (ccz), are equivalent options that are also more suited for implementing some quantum algorithms, for instance, those with coherent classical subroutines. Here, we calculate error rates and resource overheads for implementing logical ccz with pieceable fault tolerance, a nontransversal method for implementing logical gates. We provide a comparison with a nonlocal magic-state scheme on a concatenated code and a local magic-state scheme on the surface code. We find the pieceable fault-tolerance scheme particularly advantaged over magic states on concatenated codes and in certain regimes over magic states on the surface code. Our results suggest that pieceable fault tolerance is a promising candidate for fault tolerance in a near-future quantum computer.

Literature mentions only incidentally a sub-Doppler contribution in the excitation spectrum of the backward fluorescence of a dense vapor. This contribution is here investigated on Cs vapor, both on the first resonance line (894 nm) and on the weaker second resonance line (459 nm). We show that in a strongly absorbing medium, the quenching of excited atoms moving towards a window irradiated under near normal incidence reduces the fluorescence on the red side of the excitation spectrum. Atoms moving slowly towards the window produce a sub-Doppler velocity-selective contribution, whose visibility is here improved by applying a frequency-modulation technique. This sub-Doppler feature, induced by a surface quenching combined with a short absorption length for the incident irradiation, exhibits close analogies with the narrow spectra appearing with thin vapor cells. We also show that a normal incidence irradiation is essential for the sub-Doppler feature to be observed, while it should be independent of the detection geometry.

We examine the dynamics associated with the miscibility-immiscibility transition of trapped two-species Bose-Einstein condensates (TBECs) of dilute atomic gases in the presence of vortices. In particular, we consider TBECs of Rb hyperfine states and Rb-Cs mixture. In the case of a singly charged vortex in only one of the condensates, there is enhancement when the vortex is present in the species which occupies the edges at phase separation. But suppression occurs when the vortex is in the species which occupies the core region. To examine the role of the vortex, we quench the interspecies interactions to drive the TBECs from miscible to immiscible phase, and use the time-dependent Gross-Pitaevskii equation to probe the phenomenon of phase separation. We also examine the effects of higher charged vortex to phase separation.

A common challenge in quantum information processing with photons is the limited ability to manipulate and measure correlated states. An example is the inability to measure picosecond-scale temporal correlations of a multiphoton state, given state-of-the-art detectors have a temporal resolution of about 100 ps. Here, we demonstrate temporal magnification of time-bin-entangled two-photon states using a time lens and measure their temporal correlation function, which is otherwise not accessible because of the limited temporal resolution of single-photon detectors. Furthermore, we show that the time lens maps temporal correlations of photons to frequency correlations and could be used to manipulate frequency-bin-entangled photons. This demonstration opens a new avenue to manipulate and analyze spectral and temporal wave functions of many-photon states.

We measure the ellipticity dependence of high-harmonic generation (HHG) from unaligned gas-phase ensembles of the five-membered ring molecules 2,3-dihydrofuran (${\mathrm{C}}_4{\mathrm{H}}_6\mathrm{O}$), furan (${\mathrm{C}}_4{\mathrm{H}}_4\mathrm{O}$), and thiophene (${\mathrm{C}}_4{\mathrm{H}}_4\mathrm{S}$). As is normally the case, the HHG emission is suppressed for increased ellipticity since the recollision wave packet leading to HHG is steered away from the parent ion for large ellipticity. However, through comparison with computations of the first step in HHG, namely, strong-field ionization (SFI), we show that the observed differences in the ellipticity dependence for the three molecular species reflect the lateral momentum distributions of the continuum electron responsible for HHG, which in turn provides information about the particular orientation between the molecular axis and the laser field that maximizes the SFI probability. Strikingly, and contrary to the conventional wisdom in the strong-field community, we find that for furan and thiophene the most probable orientation for SFI occurs when the electric field of the laser is aligned near a nodal plane of the corresponding ionizing orbital. 2,3-dihydrofuran, on the other hand, follows the standard expectation that the most probable orientation for SFI occurs when the electric field is aligned away from any nodal plane.

In the tunneling regime for strong laser field ionization of atoms, experimental studies have shown that a substantial fraction of atoms survive the laser pulse in many Rydberg states. To explain the origin of such trapping of population into Rydberg states, two mechanisms have been proposed: the first involves ac-Stark-shifted multiphoton resonances, and the second, called frustrated tunneling ionization, leads to the recombination of tunneled electrons into Rydberg states. We use a very accurate spectral method based on complex Sturmian functions to solve the time-dependent Schrödinger equation for hydrogen in a linearly polarized infrared pulse and to calculate the tunneling probability in terms of the atomic ground-state width. We examine the probability of excitation into Rydberg states as a function of the peak intensity for various pulse durations and two wavelengths, 800 and 1800 nm, and we try to explain the results in light of the two aforementioned mechanisms. For long pulses of 800 nm wavelength, the extreme sensitivity of the trapping of population into high-lying Rydberg states to the peak intensity, the well-defined value, and parity of the angular momentum of the populated Rydberg states and the presence of Freeman resonances can be explained using a multiphotonic excitation mechanism. For strong pulses of 1800 nm wavelength, in the so-called adiabatic or quasistatic tunneling regime, the oscillations of the excitation probability as a function of intensity are in phase opposition to the ionization probability, and we observe a migration toward high values of the angular momentum with different distributions in the angular momentum at the maxima and minima of the oscillations. We also present a detailed study of how the excited-state wave packet builds up in time during the interaction of the atom with the pulse.

Interaction with the surrounding medium modifies the optical response of embedded metal clusters. For clusters from about ten to a few hundreds of silver atoms, embedded in rare-gas matrices, we study the environment effect within the matrix random phase approximation with exact exchange (RPAE) quantum approach, which has proved successful for free silver clusters. The polarizable surrounding medium screens the residual two-body RPAE interaction, adds a polarization term to the one-body potential, and shifts the vacuum energy of the active delocalized valence electrons. Within this model, we calculate the dipole oscillator strength distribution for Ag clusters embedded in helium droplets, neon, argon, krypton, and xenon matrices. The main contribution to the dipole surface plasmon red shift originates from the rare-gas polarization screening of the two-body interaction. The large size limit of the dipole surface plasmon agrees well with the classical prediction.

Coherent quantum control over many-particle quantum systems requires high-fidelity dynamics. One way of achieving this is to use adiabatic schemes where the system follows an instantaneous eigenstate of the Hamiltonian over time scales that do not allow transitions to other states. This, however, makes control dynamics very slow. Here we introduce another concept that takes advantage of preventing unwanted transitions in fermionic systems by using Pauli blocking: excitations from a protected ground state to higher-lying states are avoided by adding a layer of buffer fermions, such that the protected fermions cannot make a transition to higher-lying excited states because these are already occupied. This allows us to speed up adiabatic evolutions of the system. We do a thorough investigation of the technique, and demonstrate its power by applying it to high-fidelity transport, trap expansion, and splitting in ultracold-atom systems in anharmonic traps. Close analysis of these processes also leads to insights into the structure of the orthogonality catastrophe phenomenon.

The Schrödinger equation for a Bose gas with repulsive contact interactions in a one-dimensional space may be solved analytically with the help of the Bethe ansatz if we impose periodic boundary conditions. It was shown that for such a system there exist many-body eigenstates directly corresponding to dark soliton solutions of the mean-field equation. The system is still integrable if one switches from the periodic boundary conditions to an infinite-square-well potential. The corresponding eigenstates were constructed by Gaudin. We analyze the weak-interaction limit of Gaudin's solutions and identify the parametrization of eigenstates strictly connected with single and multiple dark solitons. Numerical simulations of measurements of the particles' positions reveal dark solitons in the weak-interaction regime and their quantum nature in the presence of strong interactions.

A point charge in the presence of a metallic nanosphere is a fundamental setup, which has implications for Raman scattering, enhancement of spontaneous emission of a molecule by an antenna, sensing, and modeling a metallic tip in proximity to a nanoparticle. Here we analytically expand the electric field of a point charge in an ${\epsilon }_2$ host medium in the presence of an ${\epsilon }_1$ sphere using the sphere eigenstates, where ${\epsilon }_1$ and ${\epsilon }_2$ can take any complex values. We develop a simple procedure to treat charge distribution, which results in a simple eigenstate expansion for the electric field of charge sources and is able to treat volume sources analytically. The electric field is strongly enhanced when ${\epsilon }_1/{\epsilon }_2$ is close to an ${({\epsilon }_1/{\epsilon }_2)}_l$ eigenvalue of a dominant mode, which is determined by the point charge location and the measurement point. An electric field exists inside the sphere when ${\epsilon }_1/{\epsilon }_2$ is close to a ${({\epsilon }_1/{\epsilon }_2)}_l$ resonance even when ${\epsilon }_1$ is a conductor. Low-order modes generate an electric field far away from the interface, where the $l=1$ mode with a resonance at ${\epsilon }_1=-2{\epsilon }_2$ generates a field at the sphere center. The high-order modes, which are associated with high spatial frequencies, become more dominant when the point charge approaches the sphere surface or when the physical parameters are close the high-order modes resonances. When ${\epsilon }_1/{\epsilon }_2$ is smaller or larger than the eigenvalues of the dominant modes, the modes interfere constructively and generate a strong signal at an angular direction equal to that of the source. The spectral information at the sphere surface may be utilized to calculate the point charge location without knowing its magnitude.

We study the problem of estimating the phase shift due to the general relativistic time dilation in the interference of photons using a nonlinear Mach-Zender interferometer setup. By introducing two nonlinear Kerr materials, one in the bottom and one in the top arm, we can measure the nonlinear phase ${\varphi }_{\text{NL}}$ produced by the space-time curvature and achieve a scaling of the standard deviation with photon number ($N$) of $1/N^{\beta }$ where $\beta >1$, which exceeds the conventional Heisenberg limit of a linear interferometer ($1/N$). The nonlinear phase shift is an effect that is amplified by the intensity of the probe field. In a regime of high photon number, this effect can dominate over the linear phase shift.