Quantum systems can be used to certify the existence of true randomness in nature, and semi-device-independent (SDI) randomness expansion has been used to achieve this goal under the prepare-measure configuration. Usually, randomness is certified with the degree of violation of some inequalities. However, the observed statistics characterizing SDI protocols contain much richer information than just a single value of the inequality. Thus, there might be a gap between the randomness in observed statistics and the randomness we certify. The purpose of this paper is to optimize the use of the full observed statistics to reduce that gap. It shows that certifying randomness directly from the full observed statistics but not some inequality is available in the SDI protocols. Besides, average of guessing probabilities should be considered as randomness quantitative standards, since it certifies more randomness than the previous maximal guessing probability method. In the analysis, we take into account the assumption that the devices and the potential adversary are classically correlated.

In engineered quantum systems, the Hamiltonian is often not completely known and needs to be determined experimentally with accuracy and efficiency. We show that this may be done at temperatures that are higher than the characteristic interaction energies, but not too much higher. The condition for this is that there are not too many multiparticle interactions: the Hamiltonian is sparse in a well-defined sense. The protocol that accomplishes this is related to compressed sensing methods of classical signal processing, in this case applied to sparse rather than low-rank matrices.

We argue that a quantum annealer at very long annealing times is likely to experience a quasistatic evolution, returning a final population that is close to a Boltzmann distribution of the Hamiltonian at a single (freeze-out) point during the annealing. Such a system is expected to correlate with classical algorithms that return the same equilibrium distribution. These correlations do not mean that the evolution of the system is classical or can be simulated by these algorithms. The computation time extracted from such a distribution reflects the equilibrium behavior with no information about the underlying quantum dynamics. This makes the search for quantum speedup problematic.

We present a detailed analysis of the Bell measurement scheme proposed in Lee et al. [Phys. Rev. Lett. 114, 113603 (2015)] based on a logical qubit using Greenberger-Horne-Zeilinger entanglement of photons. The success probability of the proposed Bell measurement can be made arbitrarily high using only linear optics as the number of photons in a logical qubit increases. We compare our scheme with all the other proposals, using single-photon qubits, coherent-state qubits, or hybrid qubits, suggested to enhance the efficiency of the Bell measurement. As a remarkable advantage, our scheme requires only photon on-off measurements, while photon number resolving detectors are necessary for all the other proposals. We find that the scheme based on coherent-state qubits shows the best performance with respect to the attained success probability in terms of the average number of photons used in the process, while our scheme outperforms the schemes using single-photon qubits. We finally show that efficient quantum communication and fault-tolerant quantum computation can be realized using our approach.

We present a realistic molecular-dynamics treatment of laser-cooled ions in radio-frequency ion traps which avoids previously made simplifications such as modeling laser cooling as a friction force and combining individual heating mechanisms into a single effective heating force. Based on this implementation, we show that infrequent energetic collisions of single ions with background gas molecules lead to pronounced heating of the entire ion ensemble and a time-varying secular ensemble temperature, which manifests itself in a superstatistical time-averaged velocity distribution of the ions. The effect of this finding on the experimental determination of ion temperatures and rate constants for cold chemical reactions is discussed.

We report on an atom interferometer based on Bragg diffraction in a fountain of alkaline-earth-metal atoms, namely ${}^{88}\mathrm{Sr}$. We demonstrate large momentum transfer to the atoms up to eight photon recoils and the use of the interferometer as a gravimeter with a sensitivity $\delta g/g=4\times {10}^{-8}$. Thanks to the special characteristics of strontium atoms for precision measurements, this result introduces alternate possibilities for experiments in fundamental and applied physics.

We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor tunneling, and angle-resolved photoemission spectroscopy (ARPES) as probes of isolated out-of-equilibrium quantum systems, and examine the crucial role played by the nonequilibrium distribution function. As an example, we focus on the induced topological time-periodic (Floquet) phase in a two-dimensional $p+ip$ superfluid, following an instantaneous quench of the coupling strength. The post-quench Cooper pairs occupy a linear combination of “ground” and “excited” Floquet states, with coefficients determined by the distribution function. While the Floquet band structure exhibits a single avoided crossing relative to the equilibrium case, the distribution function shows a population inversion of the Floquet bands at low energies. For a realization in ultracold atoms, these two features compensate, producing a bulk average rf signal that is well captured by a quasiequilibrium approximation. In particular, the rf spectrum shows a robust gap. The single crossing occurs because the quench-induced Floquet phase belongs to a particular class of soliton dynamics for the BCS equation. The population inversion is a consequence of this, and ensures the conservation of the pseudospin winding number. As a comparison, we compute the rf signal when only the lower Floquet band is occupied; in this case, the gap disappears for strong quenches. The tunneling signal in a solid-state realization is ignorant of the distribution function, and can show wildly different behaviors. We also examine rf, tunneling, and ARPES for weak quenches, such that the resulting topological steady state is characterized by a constant nonequilibrium order parameter. In a system with a boundary, tunneling reveals the Majorana edge states. However, the local rf signal due to the edge states is suppressed by a factor of the inverse system size, and is spatially deconfined throughout the bulk of the sample.

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined. Other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. The possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.

A system of $N_a$ atoms of $n$ levels interacting dipolarly with $\ell$ modes of an electromagnetic field is considered. The energy surface of the system is constructed from the direct product of the coherent states of $\mathrm{U}\left(n\right)$ in the totally symmetric representation for the matter times the $\ell$ coherent states of the electromagnetic field. A variational analysis shows that the collective region is divided into $\ell$ zones, inside each of which only one mode of the electromagnetic field contributes to the ground state. In consequence, the polychromatic phase diagram for the ground state naturally divides itself into monochromatic regions. For the case of three-level atoms in the $\mathrm{\Xi }$ configuration in the presence of two modes, the variational calculation is compared with the exact quantum solution showing that both are in agreement.

We describe a two-photon quantum interference effect which differs from the Hong-Ou-Mandel effect in that the destructive quantum inference occurs on a component of the state where two photons are in a single output mode while maintaining the two-photon events in the alternative mode. This effect is manifestly nonclassical but requires more sophisticated technology to observe than the Hong-Ou-Mandel effect. The theory outlined in this paper can also be used to classify two-photon states into classes which are related by the ability to transform the states within the class by using only linear optical interactions. This theory shows that there is an infinite number of these classes of two photon states when there are two or more modes which can support the photons.

We derive analytic expressions for the on-resonant cavity scale factor enhancement dependence on temperature, $S_0\left(T\right)$, for an intracavity medium with a Gaussian absorption resonance. Results are expressed as functions of the cavity parameters and the two resonance parameters: ${\alpha }_0\left(T\right)$, the peak absorption coefficient, and ${\mathrm{\Gamma }}_{\alpha }^R\left(T\right)$, the resonance width. A semiempirical model is developed for the temperature-dependent absorption coefficient, ${\alpha }_F(\mathrm{\Delta },T)$, in an alkali-metal-atom vapor cell, and is used to compare the predicted behavior of ${\alpha }_0\left(T\right)$ and ${\mathrm{\Gamma }}_{\alpha }^R\left(T\right)$ with the measured values for the $D{}_{2}F=2\to F^{\prime }$ resonance in ${}^{87}\mathrm{Rb}$, over the temperature range 298–325 K. Measurements of $S_0\left(T\right)$ in a low-finesse ring cavity, using the same vapor cell as the intracavity dispersive medium, were performed and found to be in agreement with the temperature-dependent behavior predicted by our theory, with quantitative agreement to 2 K for the critical temperature. The practical range of $S_0$ is found to be limited by the achievable temperature stability of the resonance parameters of the dispersive medium.

Coupling light to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of interacting quasiparticles, termed Rydberg polaritons. We derive a one-dimensional model describing the time evolution of these polaritons under paraxial propagation conditions. Specifically, we obtain a master equation governing the dynamics of Rydberg polaritons and identify conditions when it can essentially be described by an effective Hamiltonian of a single-species polariton. We verify this Hamiltonian by numerical two-excitation simulations. Under typical stationary EIT conditions it is impossible to reach the strongly interacting regime where long-range density-density correlations emerge. In contrast, by employing the time dependence of the control field the regime of strong interactions can be reached where the polaritons attain quasicrystalline order. We provide a physical explanation for the differences between stationary and time-dependent schemes.

The theoretical description of dynamics in open quantum systems becomes very demanding upon inclusion of non-Markovian effects. To simplify the computational implementation for density matrix equations of motion, the secular approximation is often applied. An experimental verification of its validity though remains difficult due to uncertainties in the system parameters and the absence of qualitatively distinct features. In this paper, we present the proposal for an experimental detection protocol sensitive to nonsecular processes neglected in the secular approximation. The protocol uses a combination of multidimensional coherent spectroscopy and nanoplasmonics. It allows for studies of nonsecular processes in various systems and provides a tool to experimentally verify the validity of the secular approximation. We apply this protocol to a system of CdSe/ZnS nanostructures and discuss the particular features originating from nonsecular processes on the resulting two-dimensional spectra.

In this work, a quantum error correction (QEC) procedure with the concatenated five-qubit code is used to construct a near-perfect effective qubit channel (with a error below ${10}^{-5}$) from arbitrary noise channels. The exact performance of the QEC is characterized by a Choi matrix, which can be obtained via a simple and explicit protocol. In a noise model with five free parameters, our numerical results indicate that the concatenated five-qubit code is general: To construct a near-perfect effective channel from the noise channels, the necessary size of the concatenated five-qubit code depends only on the entanglement fidelity of the initial noise channels.

We report on the measurement of double-differential distribution of soft electron emission from ${\text{C}}_{60}$ fullerene, induced by a fast-moving Coulomb field of 76 MeV energy bare fluorine ions. A broad “plasmon-electron” peak, riding on the Coulomb-ionization continuum, is observed due to the deexcitation of the giant dipole plasmon resonance state in ${\text{C}}_{60}$. The angular distribution of the plasmon electrons goes through a dip around ${90}^{\circ }$, which is contrary to that observed in ion-atom collisions measured in situ, indicating the alignment of the induced dipole moment along the projectile beam direction. A model based on the photoelectron angular distribution which is modified due to the ion-induced postcollisional interaction provides an excellent agreement with the observed asymmetric distribution. The distribution smoothly changes from a dip at ${90}^{\circ }$ to a peak with the variation of ejected electron energy indicating transition from a collective plasmon behavior of the whole system to a single ion-atom interaction. The single-differential cross section was also derived, which preserves the signature of the collective excitation.

We present a comprehensive study of the discretized modes of an atomic gas in different conditions of confinement. Starting from the equations of hydrodynamics we derive a closed equation for the velocity field, depending on the adiabatic and isothermal compressibilities and applicable to different dimensions and quantum statistics. At zero temperature the equation reproduces the irrotational behavior of superfluid hydrodynamics. It is also applicable above the critical temperature in the collisional regime, where the appearance of rotational components in the velocity field is caused by the external potential. In the presence of harmonic trapping, a general class of analytic solutions is obtained for systems exhibiting a polytropic equation of state, characterized by a power law isoentropic dependence of the pressure on the density. Explicit results for the compressional modes are derived for both Bose and Fermi gases in the pancake and cigar as well as in the deep two- and one-dimensional regimes. Our results agree with the analytical predictions available in the literature in some limiting cases. They are particularly relevant in one-dimensional configurations, where the study of the collective frequencies could provide a unique test of the achievement of the collisional regime at finite temperature.

Quantum optics in combination with integrated optical devices shows great promise for efficient manipulation of single photons. New physical concepts, however, can only be found when these fields truly merge and reciprocally enhance each other. Here we work at the merging point and investigate the physical concept behind a two-coupled-waveguide system with an integrated parametric down-conversion process. We use the eigenmode description of the linear system and the resulting modification in momentum conservation to derive the state generation protocol for this type of device. With this new concept of state engineering, we are able to effectively implement a two-in-one waveguide source that produces the useful two-photon NOON state without extra overhead such as phase stabilization or narrow-band filtering. Experimentally, we benchmark our device by measuring a two-photon NOON state fidelity of $\mathcal{F}=(84.2\pm 2.6)\%$ and observe the characteristic interferometric pattern directly given by the doubled phase dependence with a visibility of ${\mathcal{V}}_{\mathrm{NOON}}=(93.3\pm 3.7)\%$.

A quantum system subjected to a strong continuous monitoring undergoes quantum jumps. This very-well-known fact hides a neglected subtlety: sharp scale-invariant fluctuations invariably decorate the jump process, even in the limit where the measurement rate is very large. This article is devoted to the quantitative study of these remaining fluctuations, which we call spikes, and to a discussion of their physical status. We start by introducing a classical model where the origin of these fluctuations is more intuitive, and then jump to the quantum realm where their existence is less intuitive. We compute the exact distribution of the spikes for a continuously monitored qubit. We conclude by discussing their physical and operational relevance.