We propose a minimal theoretical model for the description of a two-dimensional (2D) strongly interacting Fermi gas confined transversely in a tight harmonic potential, and present accurate predictions for its zero-temperature equation of state and breathing mode frequency based on existing auxiliary-field quantum Monte Carlo data. We show that the minimal model Hamiltonian needs at least two independent interaction parameters, the 2D scattering length and effective range of interactions, to quantitatively explain recent experimental measurements with ultracold 2D fermions. We resolve in a satisfactory way the puzzling experimental observations of the smaller than expected equations of state and breathing mode frequency. Our establishment of the minimal model for 2D fermions is crucial to understand the Berezinskii-Kosterlitz-Thouless transition in the strongly correlated regime.

In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional (1D) photonic crystal and a metal. We show that when the system is topologically nontrivial there is a single Tamm state in each of the band gaps, whereas if it is topologically trivial the band gaps host no Tamm states. We connect the disappearance of the Tamm states with a topological transition from a topologically nontrivial system to a topologically trivial one. This topological transition is driven by the modification of the dielectric functions in the unit cell. Our interpretation is further supported by an exact mapping between the solutions of Maxwell's equations and the existence of a tight-binding representation of those solutions. We show that the tight-binding representation of the 1D photonic crystal, based on Maxwell's equations, corresponds to a Su-Schrieffer-Heeger–type model (SSH model) for each set of pairs of bands. By expanding this representation near the band edge we show that the system can be described by a Dirac-like Hamiltonian. It allows one to characterize the topology associated with the solution of Maxwell's equations via the winding number. In addition, for the infinite system, we provide an analytical expression for the photonic bands from which the band gaps can be computed.

Quantum error-correcting codes can be cast in a way which is strikingly similar to a quantum heat engine undergoing an Otto cycle. In this paper, we strengthen this connection further by carrying out a complete assessment of the thermodynamic properties of four-stroke operator-based error-correcting codes. This includes an expression for the entropy production in the cycle which, as we show, contains clear contributions stemming from the different sources of irreversibility. To illustrate our results, we study a classical three-qubit error-correcting code, well suited for incoherent states, and the nine-qubit Shor code capable of handling fully quantum states. We show that the work cost associated with the correction gate is directly associated with the heat introduced by the error. Moreover, the work cost associated with encoding and decoding quantum information is always positive, a fact which is related to the intrinsic irreversibility introduced by the noise. Finally, we find that correcting the coherent (and thus genuinely quantum) part of a quantum state introduces substantial modifications related to the Hadamard gates required to encode and decode coherences.

We study a class of gauge fixings of the Bacon-Shor code at the circuit level, which includes a subfamily of generalized surface codes. We show that for these codes, fault tolerance can be achieved by direct measurements of the stabilizers. By simulating our fault-tolerant scheme under biased noise, we show the possibility of optimizing the performance of the surface code by stretching the bulk stabilizer geometry. To decode the syndrome efficiently and accurately, we generalize the union-find decoder to biased noise models. Our decoder obtains a $0.83\%$ threshold value for the surface code in quadratic time complexity.

Thallium monofluoride is a prime candidate molecule for precision measurements aimed at discovering new physics. Optical cycling on the $B\leftarrow X$ transition around 271 nm enhances this potential. Hyperfine resolved ultraviolet spectra have been reported to determine the degree of rotational level mixing in the $B$ state and the efficiency of laser cooling on the $B\leftarrow X$ transition [Norrgard et al., Phys. Rev. A 95, 062506 (2017)]. Using these high-resolution spectra, the hyperfine structure in the $B$ state of TlF is reanalyzed and the magnitude of the $\mathrm{\Lambda }$ doubling in the $B$ state is discussed.

The Riemann hypothesis, one of the most important open problems in pure mathematics, implies the most profound secret of prime numbers. One of the most interesting approaches to solving this hypothesis is to connect the problem with the spectrum of the physical Hamiltonian of a quantum system. However, none of the proposed quantum Hamiltonians has been experimentally feasible. Here we report an experiment using a Floquet method to identify the first nontrivial zero of the Riemann $\zeta$ function and the first two zeros of Pólya's function. Through properly designed periodically driving functions, the zeros of these functions are characterized by the occurrence of crossings of quasienergies when the dynamics of the system is frozen. The experimentally obtained zeros are in good agreement with their exact values. Our study provides the experimental realization of the Riemann zeros in a quantum system, which may provide insights into the connection between the Riemann function and quantum physics.

Recent studies have confirmed the coupling of optical vortices, such as Laguerre-Gaussian and Bessel-Gaussian modes, to quadrupole-active atomic transitions. This interaction has been shown to be enhanced considerably in the case of Laguerre-Gaussian beams due to the gradient coupling, particularly, in the case of a relatively large winding number. Here, we consider the trapping and the dynamics of atoms in the optical quadrupole potential generated by two coaxial counterpropagating optical vortex beams. We focus on the atomic transition $6{}^2{S}_{1/2}\to 5{}^2{D}_{5/2}$ in Cs which is a dipole-forbidden but a quadrupole-allowed transition. We show how this atomic transition engages with the optical vortex fields at near resonance, leading to atom trapping in the optical quadrupole potential well accompanied by translational motion. We show how the optical forces generate the motion of the atoms trapped within the quadrupole potential, illustrating the results using typical experimentally accessible parameters.

Particle-wave duality has allowed physicists to establish atomic interferometers as celebrated complements to their optical counterparts in a broad range of quantum devices. In particular, interactions give rise to multiparticle correlations unavailable in linear interferometers. Here, we show that interactions lead to dynamical quantum phase transitions (DQPTs) between NOON states in an atomic interferometer. These transition points result from zeros of the Loschmidt echo, which approach the real axis of the complex time plane in the large-particle-number limit, and signify pair condensates, another type of exotic quantum states featured with prevailing two-body correlations. Such DQPTs thus provide us with a new angle to understand many-body states emergent from quantum nonequilibrium dynamics. Our work also suggests interacting atomic interferometers as a new tool for creating highly entangled states to beat the standard quantum limit.

Turbulence in the quantum (superfluid) regime, similarly to its classical counterpart, continues to attract a great deal of scientific inquiry due to the yet high number of unresolved problems. While turbulent states can be routinely created in degenerate atomic gases, there is no generic scheme to produce turbulence in fluids of light. Under paraxial propagation, light in bulk nonlinear media behaves as a two-dimensional superfluid, described by a nonlinear Schrödinger equation formally equivalent to the Gross-Pitaevskii model of a weakly interacting Bose gas, where photon-photon interactions are mediated by a third-order (Kerr) nonlinearity. Here we develop the theory describing the onset of a kinetic instability when two paraxial optical fluids with different streaming velocities interact via the optical nonlinearity. From numerical simulations of the nonlinear Schrödinger equation, we further characterize the onset of the instability and describe its saturation in the form of vortex nucleation and excitation of turbulence. The experimental observation of such effects is also discussed. The class of instabilities described here thus provide a natural route towards the investigation of quantum (superfluid) turbulence, structure formation, and out-of-equilibrium dynamics in superfluids of light.

We measured the Kr photoelectron spectrum in the region close to the $3p$ ionization threshold. Our high-resolution measurements allowed a clear observation of spectral structures due to electron correlation effects. Analysis based on relativistic multiconfiguration calculations could explain these observed peaks as due to strong configuration interactions between the $3p^{-1}$ state and $3d^{-2}nl$ states. Calculated and experimental data for peak assignments and intensity distributions are in good agreement. In addition, we measured the anisotropy parameter $\beta$, which also agreed well with theory. These findings provide a detailed view of strong configuration interactions between the $3p^{-1}$ and $3d^{-2}nl$ inner-shell hole states.

We introduce a method for efficient, in situ characterization of linear-optical networks (LONs) in randomized boson-sampling (RBS) experiments. We formulate RBS as a distributed task between two parties, Alice and Bob, who share two-mode squeezed-vacuum states. In this protocol, Alice performs local measurements on her modes, either photon counting or heterodyne. Bob implements and applies to his modes the LON requested by Alice; at the output of the LON, Bob performs photon counting, the results of which he sends to Alice via classical channels. In the ideal situation, when Alice does photon counting, she obtains from Bob samples from the probability distribution of the RBS problem, a task that is believed to be classically hard to simulate. When Alice performs heterodyne measurements, she converts the experiment to a problem that is classically efficiently simulable, but more importantly enables her to characterize a lossy LON on the fly, without Bob's knowledge and without changing anything at Bob's end (this is what we mean by in situ). We introduce and calculate the fidelity between the joint states shared by Alice and Bob after the ideal and lossy LONs as a measure of distance between the two LONs. Using this measure, we obtain an upper bound on the total variation distance between the ideal probability distribution for the RBS problem and the probability distribution achieved by a lossy LON. Our method displays the power of the entanglement of the two-mode squeezed-vacuum states: The entanglement allows Alice to choose for each run of the experiment between RBS and a simple characterization protocol based on first-order coherence between complex amplitudes.

We have studied two-electron one-photon transitions in dielectronic recombination with H-like ions ($Z=5–54$) within ab initio QED theory. It was found that interference between dielectonic recombination with two-electron one-photon transitions and radiative recombination is prominent for light and medium ions being large enough for experimental observation. The interference manifests itself firstly in a sharp Fano-like resonance structure and secondly in a noticeable distortion of the photon angular distribution of the radiative recombination.

We study clusters of the type $A_N{B}_M$ with $N\le M\le 3$ in a two-dimensional mixture of $A$ and $B$ bosons, with attractive $AB$ and equally repulsive $AA$ and $BB$ interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced $AABB$ and $AAABBB$ clusters break into $AB$ dimers. Calculating the $AAABBB$ hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced $ABB$ trimer, $ABBB$ tetramer, and $AABBB$ pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2a_{BB}$, where the atom-dimer interaction switches to repulsion.

Entanglement-assisted random access codes (EARACs) compress a large amount of bits, such that any chosen one of them can be recovered with a large probability of success. They have been used for information theoretic treatments of semi-device-independent randomness certification and other communication complexity problems. For high-dimensional problems, the access request distribution can be used to obtain better performance, which until now could only be achieved through numerical methods. This paper makes an analytical account of access request distribution for arbitrary input sizes. We introduce entanglement-assisted almost-random access codes (EAARACs), which maximize the average probability of access under an arbitrary distribution of requests, thus refining EARACs and generalizing the methods used in the study of low-dimensional communication complexity problems. We analytically find the optimal probability of success for EAARACs under arbitrary request distributions and provide an illustrative numerical example.

Quantum de Finetti theorem indicates that a surprising connection exists between the permutation-invariant property of a large system and the independent, identical distribution that describes its subsystems. The theorem is highly nontrivial in that it allows one to infer independence—within a finite error—from symmetry alone, both of which are important and fundamental concepts in physics and mathematics. Here, we present an improved quantum de Finetti theorem that provides a lower error bound, thus establishing an even closer relationship between symmetry and independence than before. As application, we study the security of quantum key distribution under the most general attacks, and show that the key rate is higher than previous ones obtained by existing trace-norm-based de Finetti theorems. Therefore, the application of the quantum de Finetti theorem in quantum information processing, as well as developing the theorem itself, is advanced here.

Correlations disguised in various forms underlie a host of important phenomena in classical and quantum systems, such as information and energy exchanges. The quantum mutual information and the norm of the correlation matrix are both considered as proper measures of total correlations. We demonstrate that, when applied to the same system, these two measures can actually show significantly different behavior except at least in two limiting cases: when there are no correlations and when there is maximal quantum entanglement. We further quantify the discrepancy by providing analytic formulas for time derivatives of the measures for an interacting bipartite system evolving unitarily. We argue that to properly account for correlations one should consider the full information provided by the correlation matrix (and reduced states of the subsystems). Scalar quantities such as the norm of the correlation matrix or the quantum mutual information can only capture a part of the complex features of correlations. As a concrete example, we show that in describing heat exchange associated with correlations neither of these quantities can fully capture the underlying physics. As a byproduct, we also prove an area law for quantum mutual information in systems with local and short-range interactions, without need to assume Markovianity or final thermal equilibrium.

We show how the standard constitutive assumptions for the macroscopic Maxwell equations can be relaxed. This is done by arguing that the Maxwellian excitation fields ($\mathit{D}$, $\mathit{H}$) should be dispensed with, on the grounds that they (a) cannot be measured, and (b) act solely as gauge potentials for the charge and current. In the resulting theory, it is only the links between the fields ($\mathit{E}$, $\mathit{B}$) and the charge and current ($\rho$, $\mathit{J}$) that matter; and so we introduce appropriate linear operator equations that combine the Gauss and Maxwell-Ampère equations with the constitutive relations, eliminating ($\mathit{D}$, $\mathit{H}$). The result is that we can admit more types of electromagnetic media, notably, these relations can allow coupling in the bulk to a homogeneous axionic material; in contrast to standard electromagnetism where any homogeneous axionlike field is completely decoupled in the bulk, and only accessible at boundaries. We also consider a wider context, including the role of topology, extended nonaxionic constitutive parameters, and treatment of Ohmic currents. A range of examples including an axionic response material is presented, including static electromagnetic scenarios, a possible metamaterial implementation, and how the transformation optics paradigm would be modified. Notably, these examples include one where topological considerations make it impossible to model using ($\mathit{D}$, $\mathit{H}$).

Ghost imaging retrieves the image of an object by using second-order correlation, and this technique studied so far has been considered in either a spatial or temporal domain, which is hard to apply to the scenario of imaging spatiotemporal dynamic objects (STDOs). Here we propose to demonstrate spatiotemporal ghost imaging and interference (STGII) for STDOs by extending the correlation theory of optical coherence into the spatiotemporal domain. We have derived the generalized analytical formula for such STGII with partially coherent pulsed beams. Through a simple example of spatiotemporal slits at different location and time, the interesting phenomena of STGII are achieved under suitable conditions and it is observed that the image quality and interference visibility are affected by both the spatial and temporal parameters of partially coherent pulsed beams.

We present a comprehensive theory of four-wave mixing in waveguide geometries, providing a rigorous description of the dynamics of both bound as well as leaky modes within a single theoretical framework. Our approach is based on the resonant-state expansion including analytical mode normalization. For bound modes, our approach agrees with the previous theory, while it results in modified nonlinear pulse propagation for leaky modes. For instance, it predicts a more efficient generation of Stokes and anti-Stokes bands with an earlier onset than expected from the previous theory for bound modes. These effects have been demonstrated numerically for a gas-filled hollow-core annulus fiber that supports leaky modes, rendering conventional bound-mode theory inappropriate for such systems. Moreover, we find that leaky modes provide modulation instability, not only in the anomalous but also in the normal dispersion regime. The modulation instability can occur for all frequencies, which is a fundamental difference to bound modes.