It is of general interest how a quantum measurement may disturb a quantum system while it gives information on the state of the system. We study a trade-off relation between the information gain and the output fidelity for a quantum nondemolition measurement scheme for photon numbers. Toward this aim, we obtain general expressions for the information gain and the output fidelity for an arbitrary initial state. We particularly investigate how these two quantities vary with measurement strength for some specific classes of states, through a single measurement or successive measurements.

The existence of incompatible measurements is a fundamental phenomenon having no explanation in classical physics. Intuitively, one considers given measurements to be incompatible within a framework of a physical theory, if their simultaneous implementation on a single physical device is prohibited by the theory itself. In the mathematical language of quantum theory, measurements are described by POVMs (positive operator valued measures), and given POVMs are by definition incompatible if they cannot be obtained via coarse-graining from a single common POVM; this notion generalizes noncommutativity of projective measurements. In quantum theory, incompatibility can be regarded as a resource necessary for manifesting phenomena such as Clauser-Horne-Shimony-Holt (CHSH) Bell inequality violations or Einstein-Podolsky-Rosen (EPR) steering which do not have classical explanation. We define operational ways of quantifying this resource via the amount of added classical noise needed to render the measurements compatible, i.e., useless as a resource. In analogy to entanglement measures, we generalize this idea by introducing the concept of incompatibility measure, which is monotone in local operations. In this paper, we restrict our consideration to binary measurements, which are already sufficient to explicitly demonstrate nontrivial features of the theory. In particular, we construct a family of incompatibility monotones operationally quantifying violations of certain scaled versions of the CHSH Bell inequality, prove that they can be computed via a semidefinite program, and show how the noise-based quantities arise as special cases. We also determine maximal violations of the new inequalities, demonstrating how Tsirelson's bound appears as a special case. The resource aspect is further motivated by simple quantum protocols where our incompatibility monotones appear as relevant figures of merit.

We present experimental results on two-qubit Rydberg-blockade quantum gates and entanglement in a two-dimensional qubit array. Without postselection against atom loss we achieve a Bell state fidelity of $0.73\pm 0.05$. The experiments are performed in an array of single Cs atom qubits with a site to site spacing of $3.8\mu \mathrm{m}$. Using the standard protocol for a Rydberg-blockade $C_Z$ gate together with single qubit operations we create Bell states and measure their fidelity using parity oscillations. We analyze the role of ac Stark shifts that occur when using two-photon Rydberg excitation and show how to tune experimental conditions for optimal gate fidelity.

Within the universal zero-range theory, we compute the three-body recombination rate to deep molecular states for two identical bosons resonantly interacting with each other and with a third atom of another species, in the absence of weakly bound dimers. The results allow for a quantitative understanding of loss resonances at finite temperature and, combined with experimental data, can be used for testing the Efimov universality and extracting the corresponding three-body parameters in a given system. Curiously, we find that the loss rate can be dramatically enhanced by the resonant heavy-heavy interaction, even for high mass ratios where this interaction is practically irrelevant for the Efimov scaling factor. This effect is important for analyzing the recent loss measurements in the Cs-Li mixture.

The total electron-impact single-ionization cross sections of Mg and ${\mathrm{Al}}^{+}$ have been calculated by Ludlow et al. [Phys. Rev. A 79, 032715 (2009)] using the time-dependent close-coupling and $R$-matrix-with-pseudostates methods. The cross-section results were found to be in good agreement with each other, but substantially smaller than those reported by several experiments. We apply the convergent close-coupling method to the problem and find a much improved agreement with experiment.

We perform an analytical investigation in the framework of generalized $K$-matrix theory of the scattering problem in tight isotropic and harmonic waveguides allowing for several open scattering channels. The scattering behavior is explored for identical bosons and fermions, as well as for distinguishable particles, the main aspect being the confinement-induced resonances (CIR) which are attributed to different partial waves. In particular, we present the unitarity bounds which emerge when considering a quasi-one-dimensional system. Unitarity bounds are also given for the transition coefficients, which show the limitations for efficient transversal (de)excitations by means of CIRs. We analyze the CIR for $d$ waves and find the intriguing phenomenon of a strong transmission suppression in the presence of more than one open channel, which represents an interesting regime to be applied in the corresponding many-particle systems. The corresponding channel threshold singularities are studied and it is shown that these are solely determined by the symmetry class of the partial wave.

The Su–Schrieffer–Heeger model of polyacetylene is a paradigmatic Hamiltonian exhibiting nontrivial edge states. By using Floquet theory we study how the spectrum of this one-dimensional topological insulator is affected by a time-dependent potential. In particular, we provide evidence of the competition among different photon-assisted processes and the native topology of the unperturbed Hamiltonian to settle the resulting topology at different driving frequencies. While some regions of the quasienergy spectrum develop new gaps hosting Floquet edge states, the native gap can be dramatically reduced and the original edge states may be destroyed or replaced by new Floquet edge states. Our study is complemented by an analysis of the Zak phase applied to the Floquet bands. Besides serving as a simple example for understanding the physics of driven topological phases, our results could find a promising testing ground in cold-matter experiments.

Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold gases has been elusive. We show that a cause of this difficulty is the relatively high percolation threshold of a speckle potential in two dimensions, resulting in strong classical localization. We propose a realistic pointlike disorder potential that circumvents this percolation limit with localization lengths that are experimentally observable. The percolation threshold is evaluated for experimentally realistic parameters, and a regime of negligible classical trapping is identified. Localization lengths are determined via scaling theory, using both exact scattering cross sections and the Born approximation, and by direct simulation of the time-dependent Schrödinger equation. We show that the Born approximation can underestimate the localization length by four orders of magnitude at low energies, while exact cross sections and scaling theory provide an upper bound. Achievable experimental parameters for observing localization in this system are proposed.

We reconsider the problem of the spontaneous emission of light by an excited atomic state. We scrutinize the survival probability of this excited state for very short times, in the so-called Zeno regime, for which we show that the dynamics is dictated by a coherent, in-phase, response of the on-shell and off-shell vacuum modes. We also develop a perturbative approach in order to interpolate between different temporal regimes: the Zeno, golden rule (linear), and Wigner-Weisskopf (exponential) regimes. We compare results obtained with the $\widehat{\mathbf{E}}·\widehat{\mathbf{x}}$ and $\widehat{\mathbf{A}}·\widehat{\mathbf{p}}$ interaction Hamiltonians, using successively the dipole approximation and the exact coupling.

Nonstationary molecular states which contain electronic coherences can be impulsively created and manipulated by using recently developed ultrashort optical and x-ray pulses via photoexcitation, photoionization, and Auger processes. We propose several stimulated-Raman detection schemes that can monitor the subsequent phase-sensitive electronic and nuclear dynamics. Three detection protocols of an x-ray broadband probe are compared: frequency-dispersed transmission, integrated photon number change, and total pulse energy change. In addition, each can be either linear or quadratic in the x-ray probe intensity. These various signals offer different gating windows into the molecular response, which is described by correlation functions of electronic polarizabilities. Off-resonant and resonant signals are compared.

We present a state-transfer protocol that is mathematically equivalent to quantum teleportation but uses classical nonseparability instead of quantum entanglement. In our implementation we take advantage of nonseparability among three parties: orbital angular momentum (OAM), polarization, and the radial degrees of freedom of a beam of light. We demonstrate the transfer of arbitrary OAM states, in the subspace spanned by any two OAM states, to the polarization of the same beam.

We theoretically investigate a scheme in which stimulated Raman scattering (SRS) can be suppressed by coherently controlling the coupling between molecular states. In conventional SRS, two laser beams at different frequencies interact resonantly with molecular vibration to induce a gain and a loss for the two beams, respectively. In our scheme, a third beam is introduced to couple the vibrational state to another coupling state. As a result, SRS is suppressed in a way analogous to electromagnetically induced transparency. We calculated the SRS signal analytically by the density matrix approach, and investigated the feasibility of this scheme for real molecular imaging. In SRS microscopy, a donut-shaped coupling laser can be used to suppress the SRS signal from the rim part of the focal spot, leading to super-resolution. Based on our numerical studies, the lateral resolution starts to be enhanced when the coupling laser intensity exceeds $0.1\mathrm{TW}/\mathrm{c}{\mathrm{m}}^2$ at picosecond pulse duration.

Recently, A. Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] performed a much-discussed experiment in which which-way information was obtained from the light in a nested Mach-Zehnder interferometer by weak measurement. The presented analysis using the two-state vector formalism drew the conclusions that the photons followed disconnected paths. We analyze this experiment using standard quantum optical methods and arrive at analytical expressions that match the experimental results without the need for such disconnected photon paths. We also propose a simple amendment to the experiment capable of displaying new phenomena, highlighting the advantages of our description.

Exact measurement of the second-order correlation function $g^{\left(2\right)}\left(t\right)$ of a light source is essential when investigating the photon statistics and the light generation process of the source. For a stationary single-mode light source, the Mandel $Q$ factor is directly related to $g^{\left(2\right)}\left(0\right)$. For a large mean photon number in the mode, the deviation of $g^{\left(2\right)}\left(0\right)$ from unity is so small that even a tiny error in measuring $g^{\left(2\right)}\left(0\right)$ would result in an inaccurate Mandel $Q$. In this work, we address the detector-dead-time effect on $g^{\left(2\right)}\left(0\right)$ of stationary sub-Poissonian light. It is then found that detector dead time can induce a serious error in $g^{\left(2\right)}\left(0\right)$ and thus in Mandel $Q$ in those cases even in a two-detector configuration. Utilizing the cavity-QED microlaser, a well-established sub-Poissonian light source, we measured $g^{\left(2\right)}\left(0\right)$ with two different types of photodetectors with different dead times. We also introduced prolonged dead time by intentionally deleting the photodetection events following a preceding one within a specified time interval. We found that the observed $Q$ of the cavity-QED microlaser was underestimated by 19% with respect to the dead-time-free $Q$ when its mean photon number was about 600. We derived an analytic formula which well explains the behavior of the $g^{\left(2\right)}\left(0\right)$ as a function of the dead time.

We demonstrate stable, long-term trapping of fermionic ${}^6\mathrm{Li}$ atoms in an optical lattice with MHz trap frequencies for use in a quantum gas microscope. Adiabatic release from the optical lattice in the object plane of a high-numerical-aperture imaging system allows a measurement of the population distribution among the lowest three bands in both radial directions with atom numbers as low as $7\times {10}^2$. We measure exponential ground band heating rates as low as 0.014(1) ${\mathrm{s}}^{-1}$ corresponding to a radial ground-state $1/e$ lifetime of $71\left(5\right)\mathrm{s}$, fundamentally limited by scattering of lattice photons. For all lattice depths above 2 recoil, we find radial ground-state lifetimes $\ge 1.6\times {10}^6$ recoil times.

We present a scheme for the practical decoy-state quantum key distribution with heralded single-photon source. In this scheme, only two-intensity decoy states are employed. However, its performance can approach the asymptotic case of using infinite decoy states. We compare it with the standard three-intensity decoy-state method, and through numerical simulations, we demonstrate its significant improvement over the three-intensity method in both the final key rate and the secure transmission distance. Furthermore, when taking statistical fluctuations into account, a very high key generation rate can still be obtained even at a long transmission distance.

We design composite controlled-phase gates, which compensate errors in the phase of a single gate. The errors can be of various natures, such as relative, absolute, or both. We present composite sequences which are robust to relative errors up to the sixth order with the number of the constituent gates growing just linearly with the desired accuracy, and we describe a method to achieve even higher accuracy. We show that the absolute error can be canceled entirely with only two gates. We describe an ion-trap implementation of our composite gates in which simultaneous cancellation of the error in both the pulse area and the detuning is achieved.

We study the entanglement of families of Unruh modes in the Bell states $|{\mathrm{\Phi }}^{\pm }\rangle =1/\sqrt{2}\left(\right|00\rangle \pm |11\rangle )$ and $|{\mathrm{\Psi }}^{\pm }\rangle =1/\sqrt{2}\left(\right|01\rangle \pm |10\rangle )$ shared by two accelerated observers and find fundamental differences in the robustness of entanglement against acceleration for these states. States ${\mathrm{\Psi }}^{\pm }$ are entangled for all finite accelerations, whereas, due to the Unruh effect, states ${\mathrm{\Phi }}^{\pm }$ lose their entanglement for finite accelerations. This is true for Bell states of two bosonic modes, as well as for Bell states of a bosonic and a fermionic mode. Furthermore, there are also differences in the degradation of entanglement for Bell states of fermionic modes. We reveal the origin of these distinct characteristics of entanglement degradation and discuss the role that is played by particle statistics. Our studies suggest that the behavior of entanglement in accelerated frames strongly depends on the occupation patterns of the constituent states, whose superposition constitutes the entangled state, where especially states ${\mathrm{\Phi }}^{\pm }$ and ${\mathrm{\Psi }}^{\pm }$ exhibit distinct characteristics regarding entanglement degradation. Finally, we point out possible implications of hovering over a black hole for these states.

Parity measurement is a central tool for many quantum information processing tasks. In this work, we propose a method to directly measure two- and four-qubit parity with low overhead in hardware and software while remaining robust to experimental imperfections. Our scheme relies on dispersive qubit-cavity coupling and photon counting that is sensitive only to intensity; both ingredients are widely realized in many different quantum computing modalities. For a leading technology in quantum computing, superconducting integrated circuits, we analyze the measurement contrast and the back action of the scheme and show that this measurement comes close enough to an ideal parity measurement to be applicable to quantum error correction.