We study measurable quantities of bosonic and fermionic mixtures on a one-dimensional ring. These few-body ensembles consist of majority atoms obeying certain statistics (Fermi or Bose) and an impurity atom in a different hyperfine state. The repulsive interactions between majority-impurity and majority-majority are varied from weak to strong. We show that the majority-impurity repulsion is mainly responsible for the loss of coherence in the strongly interacting regime. The momentum distribution follows the $\mathcal{C}/p^4$ universal behavior for the high-momentum tail, but the contact $\mathcal{C}$ is strongly dependent on the strength of the majority-impurity and in a different way on the majority-majority interactions. The static structure factor of the majority atoms exposes a low-momentum peak for strong majority-impurity repulsion, which is attributed to an effective attraction not expected for purely repulsive forces.

We generalize the Landau-Khalatnikov hydrodynamic theory for superfluid helium to two-component (binary) Bose mixtures at arbitrary temperatures. In particular, we include the spin-drag terms that correspond to viscous coupling between the clouds. Therefore, our theory not only describes the usual collective modes of the individual components, e.g., first and second sound, but also results in new collective modes, where both constituents participate. We study these modes in detail and present their dispersions using thermodynamic quantities obtained within the Popov approximation.

In two-component Bose-Einstein condensates, the one-axis twisting Hamiltonian leads to spin squeezing with a limitation that scales with the number of atoms as $N^{-2/3}$. We propose a scheme to transform the one-axis twisting Hamiltonian into a two-axis twisting Hamiltonian, resulting in enhanced spin squeezing proportional to $N^{-1}$ approaching the Heisenberg limit. Instead of pulse sequences, only one continuous driving field is required to realize such a transformation, thus the scheme is promising for experimental realization of a two-axis twisting Hamiltonian. Quantum information processing and quantum metrology may benefit from this method in the future.

Amplified ultrashort laser pulses are useful in many fields of science and engineering. We propose a quantum approach to ultrashort pulse generation using transient quantum coherence that predicts order of magnitude stronger pulses generated with lower input energy than in the steady-state regime. This femtosecond quantum-coherent analog of nanosecond $Q$ switching is not limited by the pulse duration constraints of the latter and, in principle, may be used for a variety of lasers including plasmon nanolasers. This approach, applied to the generation of giant plasmon pulses, could achieve quantum control of plasmon relaxation dynamics by varying the drive-pulse delay, amplitude, and duration. This holds promise for a new control mechanism. We discuss implementations and applications of this source of ultrashort nano-optical studies.

We provide a systematic treatment of $N$-photon transport in a waveguide coupled to a local system using the input-output formalism. The main result of the paper is a general connection between the $N$-photon S matrix and the Green's functions of the local system. We also show that the computation can be significantly simplified by exploiting the connectedness structure of both the S matrix and the Green's function, and by computing the Green's function using an effective Hamiltonian that involves only the degrees of freedom of the local system. We illustrate our formalism by computing $N$-photon transport through a cavity containing a medium with Kerr nonlinearity, with $N$ up to 3.

In the circuit quantum electrodynamics architecture, both the resonance frequency and the coupling of superconducting qubits to microwave field modes can be controlled via external electric and magnetic fields to explore qubit-photon dynamics in a wide parameter range. Here, we experimentally demonstrate and analyze a scheme for tuning the coupling between a transmon qubit and a microwave resonator using a single coherent drive tone. We treat the transmon as a three-level system, with the qubit subspace defined by the ground and the second excited states. If the drive frequency matches the difference between the resonator and the qubit frequencies, a Jaynes-Cummings-type interaction is induced, which is tunable in both amplitude and phase. We show that coupling strengths of about 10 MHz can be achieved in our setup, limited only by the anharmonicity of the transmon qubit. This scheme has been successfully used to generate microwave photons with a controlled temporal shape [M. Pechal et al., Phys. Rev. X 4, 041010 (2014)] and can be directly implemented with superconducting quantum devices featuring larger anharmonicity for higher coupling strengths.

We analyze a model where a closed $V$ system is excited by two uncorrelated partially coherent fields. We use a collisionally broadened cw laser, which is a good model for an experimentally realizable partially coherent field, and show that it is possible to generate excited-state coherences even if the two fields are uncorrelated. This transient coherence can be increased if splitting between the excited states is reduced relative to the radiation coherence time ${\tau }_d$. For small excited-state splitting, one can use this scheme to generate a long-lived coherent response in the system.

Based on recently introduced efficient quantum state tomography schemes, we propose a scalable method for the tomography of unitary processes and the reconstruction of one-dimensional local Hamiltonians. As opposed to the exponential scaling with the number of subsystems of standard quantum process tomography, the method relies only on measurements of linearly many local observables and either (a) the ability to prepare eigenstates of locally informationally complete operators or (b) access to an ancilla of the same size as the to-be-characterized system and the ability to prepare a maximally entangled state on the combined system. As such, the method requires at most linearly many states to be prepared and linearly many observables to be measured. The quality of the reconstruction can be quantified with the same experimental resources that are required to obtain the reconstruction in the first place. Our numerical simulations of several quantum circuits and local Hamiltonians suggest a polynomial scaling of the total number of measurements and post-processing resources.

We analyze a system coupled to a bath of independent harmonic oscillators. We transform the bath in chain structure by solving an inverse eigenvalue problem. We solve the equations of motion for the collective variables defined by this transformation, and we derive the exact dynamics for a harmonic oscillator in terms of the microscopic motion of the environmental modes. We compare this approach to the well-known generalized Langevin equation and we show that our dynamics satisfies this equation.

We study the effect of $\mathcal{PT}$-symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with $\mathcal{PT}$-symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the $\mathcal{PT}$-symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for the absence or existence of the perfect reflection at one and two resonant frequencies. Our study can help us to understand the interplay between the Fano resonance and $\mathcal{PT}$ symmetry in non-Hermitian discrete systems, which may be realizable in optical waveguide experiments.

We study the discrimination of $N$ mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value. After considering the discrimination of $N$ states in a $d$-dimensional Hilbert space, we focus on the discrimination of qubit states. We develop a method to determine an optimal measurement for discriminating arbitrary qubit states, taking into account that often the optimal measurement is not unique and the maximum probability of correct results can be achieved by several different measurements. Analytical results are derived for a number of examples, mostly for the discrimination between qubit states which possess a partial symmetry, but also for discriminating $N$ equiprobable qubit states and for the dicrimination between a pure and a uniformly mixed state in $d$ dimensions. In the special case where the fixed rate of inconclusive results is equal to zero, our method provides a treatment for the minimum-error discrimination of arbitrary qubit states which differs from previous approaches.

Multipartite entanglement constitutes one of the key resources in quantum information processing. We exploit correlation tensor norms to develop a framework for its experimental detection without the need for shared frames of reference. By bounding these norms for partially separable states and states of limited dimension, we achieve an extensive characterization of entanglement in multipartite systems in an experimentally feasible way. Furthermore, we show that both bi- and multipartite dimensionality of entanglement can be revealed by our methods.

A variational method for calculating the critical nuclear charge $Z_C$ required for the binding of a nucleus to two electrons is reported. The method is very effective and performs well compared to the traditional variational principle for calculating energy. The critical nuclear charge, which corresponds to the minimum charge required for the atomic system to have at least one bound state, has been calculated for heliumlike systems with both infinite and finite nuclear masses. The value of $Z_C=0.9110282\left(3\right)$ is in very good agreement with recent values in the literature for two-electron atoms with an infinite nuclear mass. When nuclear motion is considered, the value for $Z_C$ varies from 0.911 030 3(2) for that with a nuclear mass of Ne (the largest heliogenic system considered) to $0.9218024\left(4\right)$ for a system with the nuclear mass of a positron. In all cases the energy varies smoothly as $Z\to 0$. It is found that for the finite nuclear mass case, in agreement with previous work for the fixed nucleus mass system, the outer electron remains localized near the nucleus at $Z=Z_C$. Additionally, the electron probability distribution is calculated to determine the behavior of the electrons at low $Z$.

We present an all-optical protocol for detecting population in a selected Rydberg state of alkali-metal atoms. The detection scheme is based on the interaction of an ensemble of ultracold atoms with two laser pulses: one weak probe pulse which is resonant with the transition between the ground state and the first excited state, and a pulse with high intensity which couples the first excited state to the selected Rydberg state. We show that by monitoring the absorption signal of the probe laser over time, one can deduce the initial population of the Rydberg state. Furthermore, it is shown that—for suitable experimental conditions—the dynamical absorption curve contains information on the initial coherence between the ground state and the selected Rydberg state. We present the results of a proof-of-principle measurement performed on a cold gas of ${}^{87}\mathrm{Rb}$ atoms. The method is expected to find application in quantum computing protocols based on Rydberg atoms.

We propose a scheme which can realize an extended two-component Bose-Hubbard model using polaritons confined in an array of optical cavities. In addition to the density-dependent interactions, this model also contains nonlinear coupling terms between the two components of the polariton. Using a mean-field calculation, we obtain the phase diagram which shows how these terms affect the transition between the Mott insulator and the superfluid phase. In addition, we employ both a perturbation approach and an exact diagonalization method to gain more insights into the phase diagram.

Under second-order degenerate perturbation theory, we show that the physics of $N$ particles with arbitrary spin confined in a one-dimensional trap in the strongly interacting regime can be described by superexchange interaction. An effective spin-chain Hamiltonian (non-translationally-invariant Sutherland model) can be constructed from this procedure. For spin-1/2 particles, this model reduces to the non-translationally-invariant Heisenberg model, where a transition between Heisenberg antiferromagnetic (AFM) and ferromagnetic (FM) states is expected to occur when the interaction strength is tuned from the strongly repulsive to the strongly attractive limit. We show that the FM and the AFM states can be distinguished by two different methods: the first is based on their distinct responses to a spin-dependent magnetic gradient, and the second is based on their distinct momentum distributions. We confirm the validity of the spin-chain model by comparison with results obtained from several unbiased techniques.

In a coupled cavity QED network model, we study the transition from a delocalized superfluidlike state to a localized Mott-insulator-like state, triggered by losses. Without cavity losses, the transition never takes place. Further, if we measure the quantum correlations between the polaritons via the negativity, we find a critical cavity damping constant, above which the negativity displays a single peak in the same time region where the transition takes place. Additionally, we identify two regions in the parameter space, where, below the critical damping, oscillations of the initial localized state are observed along with a multipeaked negativity, while, above the critical value, the oscillations die out and the transition is witnessed by a neat single peaked negativity.

A modular systematic analysis of the feasibility of modifying atomic transition rates by tailoring the electromagnetic field of an external coherent light source is presented. The formalism considers both the center of mass and internal degrees of freedom of the atom, and all properties of the field: frequency, angular spectrum, and polarization. General features of recoil effects for internal forbidden transitions are discussed. A comparative analysis of different structured light sources is explicitly worked out. It includes spherical waves, Gaussian beams, Laguerre-Gaussian beams, and propagation invariant beams with closed analytical expressions. It is shown that increments in the order of magnitude of the transition rates for Gaussian and Laguerre-Gaussian beams, with respect to those obtained in the paraxial limit, require waists of the order of the wavelength, while propagation invariant modes may considerably enhance transition rates under more favorable conditions. For transitions that can be naturally described as modifications of the atomic angular momentum, this enhancement is maximal (within propagation invariant beams) for Bessel modes, Mathieu modes can be used to entangle the internal and center-of-mass involved states, and Weber beams suppress this kind of transition unless they have a significant component of odd modes. However, if a recoil effect of the transition with an adequate symmetry is allowed, the global transition rate (center of mass and internal motion) can also be enhanced using Weber modes. The global analysis presented reinforces the idea that a better control of the transitions between internal atomic states requires both a proper control of the available states of the atomic center of mass, and shaping of the background electromagnetic field.

We explore theoretically the optical response properties in an optomechanical system under an electromagnetically induced transparency condition but with the mechanical resonator being driven by an additional coherent field. In this configuration, more complex quantum coherent and interference phenomena occur. In particular, we find that the probe transmission spectra depend on the total phase of the applied fields. Our study also provides an efficient way to control propagation of a probe field from perfect absorption to remarkable amplification.