When a two-component Bose-Einstein condensate is placed into rotation, a lattice of vortices and cores appear. The geometry of this lattice (triangular or square) varies according to the rotational value and the intercomponent coupling strengths. In this paper, assuming a Thomas-Fermi regime, we derive a point energy that allows us to determine for which values of the parameters the lattice goes from triangular to square. It turns out that the separating curve in the phase diagram agrees fully with the complete numerical simulations of the Gross-Pitaevskii equations. We also derive a formula for the critical velocity of appearance of the first vortex and prove that the first vortex always appears first in the component with largest support in the case of two disks, and we give a criterion in the case of disk and annulus.

We use microscopic many-body theory to analyze the problem of itinerant ferromagnetism in a repulsive atomic Fermi gas of hard spheres. Using simple arguments we show that the available theoretical predictions for the onset of the ferromagnetic transition predict a transition point at a density ($k_{F}a\sim 1$) that is too large to be compatible with the universal low-density expansion of the energy. We present variational calculations for the hard-sphere Fermi gas, in the framework of Fermi hypernetted chain theory, that shift the transition to higher densities ($k_{F}a\sim 1.8$). Backflow correlations, which are mainly active in the unpolarized system, are essential for this shift.

As previous theoretical results recently revealed, a Kramers-Kronig transform of multiphoton absorption rates allows for a precise prediction on the dispersion of the nonlinear refractive index $n_2$ in the near infrared. It was shown that this method allows reproduction of recent experimental results on the importance of the higher-order Kerr effect. Extending these results, the current manuscript provides the dispersion of $n_2$ for all noble gases in excellent agreement with reference data. It is furthermore established that the saturation and inversion of the nonlinear refractive index is highly dispersive with wavelength, which indicates the existence of different filamentation regimes. While shorter laser wavelengths favor the well-established plasma clamping regime, the influence of the higher-order Kerr effect (HOKE) dominates in the long-wavelength regime.

We experimentally study the statistics of two-photon speckle patterns, obtained when spatially entangled photon pairs are scattered through a random medium. Striking differences arise between the scattering of highly entangled states and almost separable states. Both the purity of the field and the Schmidt number, which quantifies the number of entangled modes, can be obtained from the visibility of the speckles. We observe nonexponential statistics for both the intensities and the two-photon correlations.

D${}_2$ and H${}_2$ Stark recurrence spectra have been measured at scaled energies of $\epsilon =-2.3$ and $\epsilon =-3.2$. An isotope shift in the scaled-action locations of recurrence peaks is found and explained by the increased density of states associated with perturbing rotational series. This reinforces the insight gained in previous work on the correspondence between the structures of a quantum spectrum and its classical periodic orbits.

The stability of an unpolarized two-component dipolar Fermi gas is studied within mean-field theory. Besides the known instability towards spontaneous magnetization with Fermi sphere deformation, another instability toward spontaneous formation of a spin-orbit coupled phase with a Rashba-like spin texture is found. A phase diagram is presented and consequences are briefly discussed.

We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method with the hitherto existing concepts for effective interactions and present physical examples for the application of our formalism, including dissipative state preparation by engineered decay processes.

Privacy amplification (PA) is an essential postprocessing step in quantum key distribution (QKD) for removing any information an eavesdropper may have on the final secret key. In this paper, we consider delaying PA of the final key after its use in one-time pad encryption and prove its security. We prove that the security and the key generation rate are not affected by delaying PA. Delaying PA has two applications: it serves as a tool for significantly simplifying the security proof of QKD with a two-way quantum channel, and also it is useful in QKD networks with trusted relays. To illustrate the power of the delayed PA idea, we use it to prove the security of a qubit-based two-way deterministic QKD protocol which uses four states and four encoding operations.

Quantum computation with photons requires efficient two-photon gates. We put forward a two-photon entangling gate which uses an intermediate atomic system. The system includes a single Rydberg atom which can switch on and off photon absorption in an ensemble using the dipole blockade. The gate is based in a counterfactual protocol. The mere possibility of an absorption that can only occur with a vanishing probability steers the photons to the desired final state.

A theoretical study of the intense-field multiphoton ionization of hydrogenlike systems is performed by solving the time-dependent Dirac equation within the dipole approximation. It is shown that the velocity-gauge results agree to the ones in the length gauge only if the negative-energy states are included in the time propagation. On the other hand, for the considered laser parameters, no significant difference is found in the length gauge if the negative-energy states are included or not. Within the adopted dipole approximation the main relativistic effect is the shift of the ionization potential. A simple scaling procedure is proposed to account for this effect.

We theoretically investigate the possibility to generate nonclassical states of optical and mechanical modes of optical cavities, distant from each other. A setup comprised of two identical cavities, each with one fixed and one movable mirror and coupled by an optical fiber, is studied in detail. We show that with such a setup there is potential to generate entanglement between the distant cavities, involving both optical and mechanical modes. The scheme is robust with respect to dissipation, and nonlocal correlations are found to exist in the steady state at finite temperatures.

Xu and Shakeshaft [Phys. Rev. A 84, 024701 (2011)] presented theoretical cross sections for excitation of the $2s$ and $2p$ states of He${}^{+}$ at low collision energies, pointing out in particular the presence of cusps at the excitation threshold. We update their discussion of the comparison between theory and experiment, and confirm that results obtained using standard $R$-matrix and two-dimensional $R$-matrix propagation techniques also show such cusps.

High-order harmonics were generated with neon gas by using 12-fs midinfrared laser pulses with stabilized carrier-envelope phase (CEP). At some specific CEP, a broad “supercontinuum” of the extreme ultraviolet spectrum can be obtained. Two distinct continuous spectral regimes are found by numerical simulation, which come from two adjacent half cycles of the laser pulse. A phase-matching mechanism for high-photon-energy harmonics of a long trajectory driven by a midinfrared laser pulse is found.

We present a measurement scheme capable of achieving the quantum limit of parameter estimation using an adaptive strategy that minimizes the parameter's variance at each step. The adaptive rule we propose makes the scheme robust against errors, in particular imperfect readouts, a critical requirement to extend adaptive schemes from quantum optics to solid-state sensors. Thanks to recent advances in single-shot readout capabilities for electronic spins in the solid state (such as nitrogen vacancy centers in diamond), this scheme can also be applied to estimate the polarization of a spin bath coupled to the sensor spin. In turns, the measurement process decreases the entropy of the spin bath resulting in longer coherence times of the sensor spin.

We derive a fundamental conservation law of operator current for master equations describing reduced quantum systems. If this law is broken, the temporal integral of the current operator of an arbitrary system observable does not yield in general the change of that observable in the evolution. We study Lindblad-type master equations as examples and prove that the application of the secular approximation during their derivation results in a violation of the conservation law. We show that generally any violation of the law leads to artificial corrections to the complete quantum dynamics, thus questioning the accuracy of the particular master equation.

Phase randomization is a very important assumption in the Bennett-Brassard 1984 quantum key distribution (QKD) system with a weak coherent source. Thus an active phase modulator is needed to randomize the phase of source. However, it is hard to check whether the phase of source is randomized totally or not in practical QKD systems. In this paper a partially random phase attack is proposed to exploit this imperfection. Our analysis shows that Eve can break the security of a two-way QKD system by using our attack, even if an active phase randomization is adopted by Alice. Furthermore, the numerical simulation shows that in some parameter regimes, our attack is immune to the one-decoy-state method.

We present system-theoretic quantum state reconstruction methods that minimize estimation error by combining optimal quantum control with asymptotically efficient estimation. Introducing the notion of optimal observability of a quantum dynamical system—a concept that does not exist in classical control theory—we formulate and solve the Pareto optimal control problem of maximizing state estimation accuracy while minimizing the expenditure of available control and measurement resources. Necessary and sufficient conditions for optimal observability, based on the quantum optimal observability Gramian, are presented. We examine the finite sample efficiency of the estimation methodology for two- and three-level systems using ideal and noisy control fields, and demonstrate the advantages of state reconstruction schemes based on optimal observability theory for experimentally realistic sample sizes. These results indicate that the optimal control of quantum measurement bases can be used to minimize state reconstruction errors by fully exploiting the information geometry of quantum states.

Dynamical decoupling is a technique for preserving the coherence of quantum-mechanical states in the presence of a noisy environment. It uses sequences of inversion pulses to suppress the environmental perturbations by periodically refocusing them. It has been shown that different sequences of inversion pulses show vastly different performance, in particular also concerning the correction of experimental pulse imperfections. Here, we investigate specifically the role of time-reversal symmetry in the building blocks of the pulse sequence. We show that using time-symmetric building blocks often improves the performance of the sequence compared to sequences formed by time-asymmetric building blocks. Using quantum state tomography of the echoes generated by the sequences, we analyze the mechanisms that lead to loss of fidelity and show how they can be compensated by suitable concatenation of symmetry-related blocks of decoupling pulses.

Recently, several hybrid approaches to quantum information emerged which utilize both continuous- and discrete-variable methods and resources at the same time. In this work, we investigate the bipartite hybrid entanglement between a finite-dimensional, discrete-variable quantum system and an infinite-dimensional, continuous-variable quantum system. A classification scheme is presented leading to a distinction between pure hybrid entangled states, mixed hybrid entangled states (those effectively supported by an overall finite-dimensional Hilbert space), and so-called truly hybrid entangled states (those which cannot be described in an overall finite-dimensional Hilbert space). Examples for states of each regime are given and entanglement witnessing as well as quantification are discussed. In particular, using the channel map of a thermal photon noise channel, we find that true hybrid entanglement naturally occurs in physically important settings. Finally, extensions from bipartite to multipartite hybrid entanglement are considered.

In this work we analyze the superfocusing of protons channeled in a $\langle 100\rangle$ Si thin crystal using the theory of crystal rainbows. The initial proton energy is 68 MeV and the proton beam incident angle is increased gradually from zero up to 30$\%$ of the critical angle for proton channeling. The reduced crystal thickness is varied around 0.250, the corresponding crystal thickness being 481.8 nm. The spatial distributions of channeled protons, obtained by the numerical solution of the proton equations of motion in the transverse position plane and a Monte Carlo computer simulation code, are explored as functions of the beam incident angle and reduced crystal thickness. They are analyzed via the corresponding mappings of the impact parameter plane to the transverse position plane, which are characterized by the rainbow effect. The performed analysis shows that it is possible to focus the beam within the region of the radius considerably below the Bohr radius. The obtained results provide the theoretical basis for the possible development of a measurement technique with the picometer resolution—the rainbow subatomic microscopy.