The overlap measurement scheme accomplishes the evaluation of the overlap of two input quantum states by only measuring an introduced auxiliary qubit, irrespective of the complexity of the two input states. We find a counterintuitive phenomenon that no quantum dissonance can be found in the process of overlap measurement scheme, even though the auxiliary qubit might be entangled, classically correlated, or even uncorrelated with the two input states based on different types of input states. In principle, this provides an opposite but supplementary example to the remarkable algorithm of the deterministic quantum computation with one qubit in which no entanglement is present but quantum dissonance is necessary. Finally, we consider a simple overlap measurement model to demonstrate the continuous change (including potential sudden death of quantum discord) of the input states from entangled to product states by only adjusting some initial parameters.

A Wigner-distribution-like (WDL) function is used to study the time-energy distribution of a photoelectron emitted from an atom in few-cycle laser fields with different frequencies. The WDL function shows the dependence of ionization probability on time and explicitly demonstrates the transition of the ionization process from the multiphoton regime to the tunneling regime with decreasing laser frequency. Accompanying this transition, the semiclassical relationship between the final drift energy and the ionization moment becomes more and more valid and is in good agreement with the time-energy distribution in the tunneling regime. Meanwhile, the photoelectron energy spectrum shows a fine structure, which is more and more dependent on the direction of the ejection of the photoelectron and the carrier-envelope phase of the laser field. Moreover, the WDL function enables us to explicitly attribute the fine structure in the tunneling regime to interference between electrons with the same kinetic energy ejected at different times.

The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously expected. The Heisenberg limit can be restored as a rigorous bound to the accuracy provided one considers the accuracy averaged over the possible values of the unknown phase, as we have recently shown [Phys. Rev. A 85, 041802(R) (2012)]. Here we present an expanded proof of this result together with a number of additional results, including the proof of a previously conjectured stronger bound in the asymptotic limit. Other measures of the accuracy are examined, as well as other restrictions on the generator of the phase shifts. We provide expanded numerical results for the minimum error and asymptotic expansions. The significance of the results claiming violation of the Heisenberg limit is assessed, followed by a detailed discussion of the limitations of the Cramér-Rao bound.

A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenović et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic evolution, we show that this construction is just a simple rescaling of the known canonical “time” or “age” observable, with the period $T$ rescaled to $2\pi$. Further, for Hamiltonians generating quasiperiodic evolution, we note that the construction leads to a phase observable having several undesirable features, including (i) having a trivially uniform probability density for any state of the system, (ii) not reducing to the periodic case in an appropriate limit, and (iii) not having any clear generalization to an infinite energy spectrum. In contrast, we note that a covariant time observable has been previously defined for such Hamiltonians, which avoids these features. We also show how this “quasiperiodic” time observable can be represented as the well-defined limit of a sequence of periodic time observables.

Ultracold atoms provide an ideal system for the realization of quantum technologies but also for the study of fundamental physical questions such as the emergence of decoherence and classicality in quantum many-body systems. Here, we study the global structure of the quantum dynamics of bosonic atoms in a double-well trap based upon the Bose-Hubbard Hamiltonian and analyze the conditions for the generation of many-particle entanglement and spin squeezing which have important applications in quantum metrology. We show how the quantum dynamics is determined by the phase-space structure of the associated mean-field system and where true quantum features arise beyond this “classical” approximation.

We consider bipartite quantum systems characterized by a continuous angular variable $\theta$, representing, for instance, the position of a particle on a circle or in a periodic lattice. For this type of system, we show how to violate inequalities similar to Clauser-Horne-Shimony-Holt (CHSH) ones, originally derived for bipartite spin-$1/2$-like systems. Such inequalities involve correlated measurement of continuous angular functions and are equivalent to the continuous superposition of CHSH inequalities acting on bidimensional subspaces of the infinite dimensional Hilbert space. As an example, we discuss in detail one application of our results, and we derive inequalities based on orientation correlation measurements. The introduced Bell-type inequalities open the perspective of new and simpler experiments to test the assumptions of locality, realism, or freedom of choice in a variety of quantum systems described by continuous variables. We discuss in detail a possible implementation using the orbital angular momentum of photons.

The decoherence rate is a nonlinear channel parameter that describes quantitatively the decay of the off-diagonal elements of a density operator in the decoherence basis. We address the question of how to experimentally access such a nonlinear parameter directly without the need for complete process tomography. In particular, we design a simple experiment working with two copies of the channel, in which the registered mean value of a two-valued measurement directly determines the value of the average decoherence rate. No prior knowledge of the decoherence basis is required.

An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low-energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian for each eigenvalue to be calculated, using perturbation expansion, and extracting the eigenvalue from the diagonalization of the effective Hamiltonian. The size of the effective Hamiltonian can be significantly smaller than that of the original Hamiltonian, hence the diagonalization can be done much faster. We compare our approximate diagonalization results with those obtained using exact diagonalization and quantum Monte Carlo calculation for random problem instances with up to 128 qubits.

The transfer of entanglement from optical fields to qubits provides a viable approach to entangling remote qubits in a quantum network. In cavity quantum electrodynamics, the scheme relies on the interaction between a photonic resource and two stationary intracavity atomic qubits. However, it might be hard in practice to trap two atoms simultaneously and synchronize their coupling to the cavities. To address this point, we propose and study entanglement transfer from cavities driven by an entangled external field to controlled flying qubits. We consider two exemplary non-Gaussian driving fields: NOON and entangled coherent states. We show that in the limit of long coherence time of the cavity fields, when the dynamics is approximately unitary, entanglement is transferred from the driving field to two atomic qubits that cross the cavities. On the other hand, a dissipation-dominated dynamics leads to very weakly quantum-correlated atomic systems, as witnessed by vanishing quantum discord.

We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem [L. K. Grover, Phys. Rev. Lett. 79, 325 (1997)] of finding a marked item inside of an unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters and is not exponentially small. This allows a significant reduction of the searching time, which is proportional to the number of qubits. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment, and we discuss alternate ways to solve $NP$-complete problems.

A calculation of the blackbody radiation shift of the B${}^{+}$ clock transition is performed. The polarizabilities of the B${}^{+}$$2s^2$ ${}^1{S}^e$, $2s2p$ ${}^1{P}^o$, and $2s2p$ ${}^3{P}^o$ states are computed using the configuration interaction method with an underlying semiempirical core potential. The recommended dipole polarizabilities are 9.64(3)$a_0^3$, 7.78(3)$a_0^3$ and 16.55(5)$a_0^3$, respectively. The derived frequency shift for the $2s^2$ ${}^1{S}^e$ $\to$ $2s2p$ ${}^3{P}_0^o$ transition at 300 K is 0.0160(5) Hz. The dipole polarizabilities agree with an earlier relativistic calculation [Safronova et al., Phys. Rev. Lett. 107, 143006 (2011)] to better than 0.2$\%$. Quadrupole and octupole polarizabilities and nonadiabatic multipole polarizabilities are also reported.

A nonperturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion of this potential, we express eigenfunctions of the two-center Hamiltonian in terms of well-known solutions of the “monopole” problem that employ solely the spherically symmetric part of the interaction. When combined with the coupled-channel method, such a wave-function–expansion technique allows for an accurate description of the electron dynamics in the field of moving ions for a wide range of internuclear distances. To illustrate the applicability of the proposed approach, the probabilities of the $K$- as well as $L$-shell ionization of hydrogen-like ions in the course of nuclear $\alpha$ decay and slow ion-ion collisions have been calculated.

We have used dipole-quadrupole interference spectroscopy to observe an optically forbidden quadrupole Rydberg series of helium autoionizing levels. The technique measures the forward-backward asymmetry of photoelectron angular distributions produced in the vacuum ultraviolet photoionization of helium. The resonant behavior of this asymmetry in the region of a quadrupole autoionizing level enables the determination of the position, width, and Fano line-profile parameter $q$ of the level. We have obtained these quantities for the He ${}_2{(1,0)}_n^{+}{}^{1}D$ Rydberg series for $n=2$–7. We find that for $n\ge 3$ all three quantities have the expected $n$ scaling, with a quantum defect of 0.31. For $n\ge 3$ the average $q$ parameter lies close to zero, whereas for $n=2$ it is negative.

We investigate the coherent collision of anisotropic quasi-two-dimensional bright solitons in dipolar Bose-Einstein condensates. Our analysis is based on the extended Gross-Pitaevskii equation, and we use the split-operator method for the grid calculations and the time-dependent variational principle with an Ansatz of coupled Gaussian functions to calculate the time evolution of the ground state. We compare the results of both approaches for collisions where initially the solitons are in the repelling side-by-side configuration and move towards each other with a specific momentum. We change the relative phases of the condensates, and introduce a total angular momentum by shifting the solitons in opposite directions along the polarization axis. Our calculations show that collisions result in breathing-mode-like excitations of the solitons.

The propagation of a weak-field pulse through a medium of three-level atoms is considered. Each atom has a $\Lambda$-type level scheme in which the two lower levels are stable. A strong control field drives one of the electronic transitions while the signal field drives the coupled transition under conditions where EIT (electromagnetically induced transparency) is usually operative. The input pulse is slowed and compressed as it enters the medium, adiabatically following the EIT solution. However, if the control field is changed suddenly when the pulse is in the medium, the signal field is transformed into two pulses, one of which propagates as a normal EIT pulse and the other with a different speed and an amplitude that oscillates in time. The temporal oscillations are transformed into both spatial and temporal oscillations as the pulse exits the medium. An analytic expression is derived for the pulse intensity which provides a good approximation to the exact result at all times. It is shown that the oscillating component of the exiting pulse can be spatially compressed in comparison with the input pulse.

Optical atomic clocks using highly charged ions hold an intriguing promise of metrology at the 19th significant figure. Here we study transitions within the $4f^{12}$ ground-state electronic configuration of highly charged ions. We consider isotopes lacking hyperfine structure and show that the detrimental effects of coupling of electronic quadrupole moments to the gradients of a trapping electric field can be effectively reduced by using specially chosen virtual clock transitions. The estimated systematic fractional clock accuracy is shown to be below ${10}^{-19}$.

We extend our previous investigations of fermionic condensation in broad Feshbach resonances by using the two-channel model developed for narrow Feshbach resonances. We investigate two crossovers: the Bardeen-Cooper-Schrieffer–Bose-Einstein condensation (BCS-BEC) crossover by changing the $s$-wave scattering length and the crossover from a narrow to a broad resonance by changing the atom-molecule coupling. At zero temperature we analyze, as a function of both atom-molecule coupling and $s$-wave scattering length, the chemical potential, the energy gap, and the condensate fraction of atoms. In particular, we predict the contribution of Cooper pairs and preformed molecules to the total condensate density along the two crossovers.

We show that variance and Shannon entropy provide contradictory conclusions for the uncertainty associated with the number operator for some families of states of harmonic oscillator systems with fixed mean number, and for the uncertainty of a spin component for states with and without fixed mean. We analyze this behavior in terms of the properties of these uncertainty measures. We explore their impact on quantum metrology, examining the limits to resolution caused by number fluctuations in diverse scenarios of phase-shift detection.

In our previous paper [D. Gonţa and P. van Loock, Phys. Rev. A 84, 042303 (2011)], we proposed an efficient scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid controlled-not gates and thus reduce complicated pulse sequences and superfluous qubit operations. In this paper, we significantly improve the output fidelity of remotely entangled atoms by introducing one additional entanglement protocol in each of the repeater nodes and by optimizing the laser beams required to control the entire scheme. Our improved distillation scheme yields an almost-unit output fidelity that, together with the entanglement distribution and swapping, opens an attractive route towards an efficient and experimentally feasible quantum repeater for long-distance quantum communication.

The emission of entangled light from planar semiconductor microcavities is studied and the entanglement properties are analyzed and quantified. Phase matching of the intracavity scattering dynamics for multiple pump beams or pulses, together with the coupling to external radiation, leads to the emission of a manifold of entangled photon pairs. A decomposition of the emitted photons into two parties leads to a strong entanglement of the resulting bipartite system. For the quantification of the entanglement, the Schmidt number of the system is determined by the construction of Schmidt number witnesses. It is analyzed to which extent the resources of the originally strongly entangled light field are diminished by dephasing in propagation channels.