The quantum router is an elementary building block in quantum information processing and quantum communication. This work constitutes a step forward in this direction, i.e., an efficient scheme is proposed for the implementation of a nonreciprocal single-photon quantum router, allowing the routing of a single photon from one side but blocking it from the other side. Our model consists of two directly coupled coplanar-waveguide resonators and a superconducting ring resonator, which are connected together through a transmission line. The nonreciprocity is realized by unidirectionally interacting the rotating microwave modes of the ring resonator with a dissipative magnon mode in an yttrium iron garnet disk. We find that a single-photon signal can be delivered from a given input port to either of the two output ports, but is fully absorbed from the opposite one. The proposed scheme not only enriches the family of nonreciprocal quantum devices, but also finds useful applications in chiral quantum technologies.

We show that the parity (evenness or oddness) of a nonclassical state of light has a dominant influence on the interference effects at a balanced beam splitter, irrespective of the state initially occupying the other input mode. Specifically, the parity of the nonclassical state gives rise to destructive interference effects that result in deep valleys in the output joint number distribution of which the Hong-Ou-Mandel (HOM) effect is a limiting case. The counterintuitive influence of even a single photon to control the output of a beam splitter illuminated by any field, be it a coherent or even a noisy thermal field, demonstrates the extraordinary power of nonclassicality. The canonical example of total destructive interference of quantum amplitudes leading to the absence of coincidence counts from a 50:50 beam splitter (BS) is the celebrated HOM effect, characterized by the vanishing of the joint probability of detecting singe photons in each of the output beams. We show that this is a limiting case of more general input states upon which a 50:50 BS can create total, or near total, destructive interference of quantum amplitudes. For the case of an odd photon-number input Fock state of arbitrary value $n>0$ we show that the joint photon-number probabilities vanish when detecting identical photon numbers in each output beams. We specifically examine the mixing of photon-number states of $n=1$, 2, and 3 with a continuous-variable state, such as a coherent state of arbitrary amplitude, and a thermal state. These vanishing joint probabilities form what we call a central nodal line: A contiguous set of zeros representing complete destructive interference of quantum amplitudes. We further show that with odd or even photon-number Fock states $n$, with $n>1$, there will be additional off-diagonal curves along which the joint photon-number probabilities are either zero, or near zero, which we call pseudonodal curves, which constitute a near, but not complete, destructive interference pattern in the photon-number space. We interpret all of these interference effects as an extension of the HOM effect. We explain the origin of these effects and explore the experimental prospects for observing them with currently available number-resolving detectors in the presence of a small amount of noise.

By representing an event as the joint state of a detector-timer couple that interacts with a system, we recover the familiar tensor product structure, used to describe spatially separated systems, in the context of timelike events. Furthermore, with this approach, we extend the superposition principle to the moment of occurrence of events. We then outline quantum signatures of causality that manifest through coherence in the detector state and correlation functions of time operators. Finally, we expand the scope of quantum information theoretic measures of state discrimination and information content, commonly used to characterize spatially separated systems, to events in spacetime. For causally connected events, we illustrate a deterministic relationship between events (akin to spatially entangled physical systems) where observing a previous event (one subsystem) enables us to delineate a later event (the other subsystem).

We show that the cross sections for a broad range of resonant inelastic processes accompanied by excitation exchange (such as spin exchange, Förster resonance, or angular momentum exchange) exhibit a near-threshold scaling $E^{\mathrm{\Delta }{m}_{12}}$, where $E$ is the collision energy, $\mathrm{\Delta }{m}_{12}=m_1^{\prime }+m_2^{\prime }-m_1-m_2$, and $m_i$ and $m_i^{\prime }$ are the initial and final angular momentum projections of the colliding species ($i=1,2$). In particular, the inelastic cross sections for $\mathrm{\Delta }{m}_{12}=0$ transitions display an unconventional $E^0$ scaling similar to that of elastic cross sections, and their rates vanish as $T^{\mathrm{\Delta }{m}_{12}+1/2}$. For collisions dominated by even partial waves (such as those of identical bosons in the same internal state) the scaling is modified to ${\sigma }_{\text{inel}}\propto E^{\mathrm{\Delta }{m}_{12}+1}$ if $\mathrm{\Delta }{m}_{12}$ is odd. We present accurate quantum scattering calculations that illustrate these modified threshold laws for resonant spin exchange in ultracold $\text{Rb}+\text{Rb}$ and ${\mathrm{O}}_2+{\mathrm{O}}_2$ collisions. Our results illustrate that the well-known $k^{-1}$ threshold scaling of inelastic cross sections only applies to exothermic, rather than resonant, inelastic processes.

Recent experiments on ultracold nonreactive dipolar molecules have observed high two-body losses, even though these molecules can undergo neither inelastic, nor reactive (as they are in their absolute ground state), nor light-assisted collisions (if they are measured in the dark). In the presence of an electric field these losses seem to be near universal (the probability of loss at short range is near unity) while in the absence of it the losses seem nonuniversal. To explain these observations we propose a simple model based on the mixing effect of an electric field on the states of the two diatomic molecules at long range and on the density of states of the tetramer complex formed at short range, believed to be responsible for the losses. We apply our model to collisions of ground-state molecules of endothermic systems, of current experimental interest.

Shortcuts to adiabaticity (STA) are a collection of quantum control techniques that achieve high fidelity outside of the adiabatic regime. Recently an extension to shortcuts to adiabaticity was proposed by the authors [Whitty, Kiely, and Ruschhaupt, Phys. Rev. Research 2, 023360 (2020)]. This method, enhanced shortcuts to adiabaticity (eSTA), provides an extension to the original STA control functions and allows effective control of systems not amenable to STA methods. It is conjectured that eSTA schemes also enjoy an improved stability over their STA counterparts. We provide numerical evidence of this claim by applying eSTA to fast atomic transport using an optical lattice and evaluating appropriate stability measures. We show that the eSTA schemes not only produce higher fidelities but also remain more stable against errors than the original STA schemes.

Nonlinear highly multimode photonic systems are ubiquitous in optics. Yet, the sheer complexity arising from the action of nonlinearity in multimode environments has posed theoretical challenges in describing these systems. In this work, we deploy concepts from optical thermodynamics to investigate the near- and far-field emission intensity patterns emerging from nonlinear waveguide arrays. An exact equation dictating the response of a nonlinear array is derived in terms of the system's invariants that act as extensive thermodynamic variables. In this respect, the near- and far-field characteristics emerging from a weakly nonlinear waveguide lattice are analytically addressed. We show that statistically, these patterns and the resulting far-field brightness are governed by the optical temperature and its corresponding chemical potential. The extensivity associated with the entropy of such configurations is discussed. The thermodynamic results presented here were found to be in good agreement with numerical simulations obtained from nonlinear coupled-mode theory.

In this work, we measure the relative Fresnel (Goos-Hänchen) phase, which is acquired after beam propagation through a two-phase ellipsometric system under total internal reflection, by using polarization tomography. This approach presents a direct measurement which provides a more powerful and complete description of the polarization state. In this sense, the relative phase can be obtained through the polarization-state reconstruction. The experimental data confirm the simulated intensity profiles and allow us to access information about the amplitude and relative phase of the polarization state instead of measuring phase effects.

We provide a comprehensive study of the energy-transfer phenomenon—populating a given energy level—in three- and four-level quantum systems coupled to two thermal baths. In particular, we examine the effects of an external periodic driving and the coherence induced by the baths on the efficiency of the energy transfer. We consider the Floquet-Lindblad and the Floquet-Redfield scenarios, which both are in the Born-Markov, weak-coupling regime but differ in the treatment of the secular approximation, and for the latter we develop an appropriate Floquet-type master equation by employing a partial secular approximation. Throughout the whole analysis we keep Lamb-shift corrections in the master equations. We observe that, especially in the Floquet-Redfield scenario, the driving field can enhance the energy-transfer efficiency compared to the nondriven scenario. In addition, unlike nondriven degenerate systems where Lamb-shift corrections do not contribute significantly to the energy transfer, in the Redfield and the Floquet-Redfield scenarios these corrections have non-negligible effects.

Among the list of major threats to quantum computation, quantum decoherence poses one of the largest because it generates losses to the environment within a computational system which cannot be recovered via error correction methods. These methods require the assumption that the environmental interaction forces the qubit state into some linear combination of qubit eigenstates. In reality, the environment causes the qubit to enter into a mixed state where the original is no longer recoverable. A promising solution to this problem bases the computational states on the low lying energy excitations within topological materials. The existence of these states is protected by a global parameter within the Hamiltonian which prevents the computational states from coupling locally and decohering. In this paper, the qubit is based on nonlocal, topological Majorana fermions (MF), and the gate operations are generated by swapping or braiding the positions of said MF. The algorithmic calculation for such gate operations is well known, but, the opposite gates-to-braid calculation is currently underdeveloped. Additionally, because one may choose from a number of different possible qubit definitions, the resultant gate operations from calculation to calculation appear different. Here, the calculations for the two- and four-MF cases are recapitulated for the sake of logical flow. This set of gates serves as the foundation for the understanding and construction of the six-MF cases. Using these, a full characterization of the system is made by completely generalizing the list of gates and transformations between possible qubit definitions. A complete description of this system is desirable and will hopefully serve future iterations of topological qubits.

We investigate the quantum dynamics of a spin chain that implements a quantum analog of Conway's Game of Life. We solve the time-dependent Schrödinger equation starting with initial separable states and analyze the evolution of quantum correlations across the lattice. We report examples of evolutions leading to all-entangled chains and/or to time oscillating entangling structures and characterize them by means of entanglement and network measures. The quantum patterns result in structures quite different from the classical ones, even in the dynamics of local observables. A peculiar instance is a structure behaving as the quantum analog of a blinker, but that has no classical counterpart.

We present an alternative, univocal characterization of the continuous transition from atomic to molecular shape in the Coulomb system constituted by two identical particles and a third particle with the opposite charge as the mass ratio of the particles varies. Applying a marginal-conditional exact factorization to a variationally optimized wave function, we construct a nonadiabatic potential-energy surface for the relative motion between the single particle and each of the identical particles in the ground state. The transition is revealed through the evolution with the mass ratio of the topography of such a surface and of the shapes of the associated marginal and conditional distributions. Our approach unifies and extends to the nonadiabatic regime the Born-Oppenheimer and charge-distribution pictures of molecular shape.

We perform valence, core-core, and core-valence nonrelativistic configuration-interaction (CI) calculations on the states belonging to the $3s^{2}3p^n$ configuration with $n=2$, 3, and 4, for ${\mathrm{P}}^{+}({}^{3}P,{}^{1}D, {}^{1}S$), $\mathrm{P}{(}^4{S}^{\circ },{}^{2}D^{\circ }, {}^{2}P^{\circ }$), and ${\mathrm{P}}^{-}({}^{3}P,{}^{1}D, {}^{1}S$) species, respectively. Excitation energies, ionization potential, and electron affinities related to these states were calculated using orbital basis sets up to $\ell =12$ and corrected with relativistic contributions. We also carry out relativistic CI calculations for the fine structure splitting of the sublevels ${}^3{P}_{0,1,2}$ and ${}^3{P}_{2,1,0}$ in ${\mathrm{P}}^{+}$ and ${\mathrm{P}}^{-}$, respectively, and both ${}^2{D}_{3/2,5/2}^{\circ }$ and ${}^2{P}_{1/2,3/2}^{\circ }$ in P, using orbital basis sets up to $\ell =3$. Systematic studies on the convergence of both nonrelativistic and relativistic CI calculations for each electronic state show the energy contributions corresponding to each CI excitation level. Our results for the excitation energies, ionization potential, and electron affinity of the ${\left(3s^{2}3p^3\right)}^4{S}^{\circ }$ ground state, as well as fine structure splittings, are in very good agreement with the experiment and give reliability to the predicted electron affinities of the ${\left(3s^{2}3p^3\right)}^2{D}^{\circ }$ and ${}^{2}P^{\circ }$ excited states of 1135(1) meV and 1040(1) meV, respectively.

Efimov physics at $p$-wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long-range interaction potential energy, but without producing a true Efimov effect. This analysis treats the total orbital angular momenta and parities, $J^{\mathrm{\Pi }}=0^{+},1^{+},1^{-}$, and $2^{-}$, for either three spin-polarized fermions ($\uparrow \uparrow \uparrow$) or two spin-up and one spin-down fermion ($\downarrow \uparrow \uparrow$). Our results for the long-range interaction in some of those cases agree with previous work by Werner and Castin and by Blume et al., namely, in cases where the $s$-wave scattering length goes to infinity. The present results extend those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and we consider additional unitarity scenarios where the $p$-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.

We theoretically investigate a Thouless pumping scheme in the one-dimensional topological Su-Schrieffer-Heeger (SSH) model for single and multiple band-gap systems when implemented in a discrete nematic liquid crystal arrangement. For an electrically controlled SSH waveguide array, we numerically demonstrate edge-to-edge light transport at low power levels. On the other hand, at higher powers, the transport is frustrated by light-induced nonlinear defect states, giving rise to robust all-optical switching.

For a standard two-level atom coupled to the quantized field of a resonant cavity, finite-temperature effects lead to thermal occupation of the cavity modes that obfuscates measurement of the quantum nature of the atom-light interaction. In this paper we demonstrate that using a hybrid system of a superconducting cavity coupled to a multilevel Rydberg atom, it is possible to observe the quantum nature of strong coupling even at finite temperatures and to exploit this coupling to permit cooling of the thermal microwave mode towards the ground state, enabling observation of coherent vacuum Rabi oscillations even at 4 K for realistic experimental parameters. Cooling for multiple atoms is also explored, showing maximal cooling for small samples, making this a viable approach to cavity cooling with potential applications in long-range coupling of superconducting qubits via thermal waveguides.

Starting with Maxwell's equations and defining normal variables in the Fourier space, we write the equations of temporal evolution of the electromagnetic field with sources in the Hamiltonian and Lagrangian forms, making explicit all intermediate steps often omitted in standard textbooks. Then, we follow the same steps to write the equations of evolution of this field along a spatial dimension in the Hamiltonian and Lagrangian forms. In this way, we arrive at the explicit form of the generator of spatial evolution of the electromagnetic field with sources and show that it has a physical meaning of the modulus of momentum transferred through a given plane orthogonal to the direction of propagation. In a particular case of free field this generator coincides with the projection of the full momentum of the field on the propagation direction, taken with a negative sign. The Hamiltonian and Lagrangian formulations of the spatial evolution are indispensable for a correct quantization of the field when considering its spatial rather than temporal evolution, in particular, for a correct definition of the equal-space commutation relations.

The presence of correlations in the input state of a noninteracting many-body quantum system can lead to an increase in the amount of work we can extract from it under global unitary processes (ergotropy). The present work explores such effect on translationally invariant systems relying on the matrix product operator formalism to define a measure of how much they are correlated. We observe that in the thermodynamic limit of large number of sites, complete work extraction can be attained for relatively small correlation strength (a reduction of a 2 factor in dB units). Most importantly, such an effect appears to not be associated with the presence of quantum correlations (e.g., entanglement) in the input state (classical correlation suffices), and to be attainable by only using incoherent ergotropy. As a byproduct of our analysis, we also present a rigorous formulation of the heuristic typicality argument first formulated by Alicki and Fannes [R. Alicki and M. Fannes, Phys. Rev. E 87, 042123 (2013)], which gives the maximum work that is extractable for a set of many identical quantum systems in the asymptotic limit.

We analyze the current of Bose particles across a tight-binding chain connected at both ends to the particles' reservoirs. Unlike the standard open Bose-Hubbard model, where the presence of reservoirs is taken into account by the Lindbladians acting on the first and last sites of the chain, we use semimicroscopic models for the reservoirs. This allows us to address the case of arbitrary reservoir temperature. In particular, we discuss the phenomenon of the resonant transmission for nearly condensed bosons, where the current across the chain is significantly enhanced for certain values of the gate voltage.