The theory of quantum state estimation is exploited here to investigate the most efficient strategies for this task, especially targeting a complete picture identifying optimal conditions in terms of Fisher information, quantum measurement, and associated estimator. The approach is specified to estimation of the phase of a qubit in a rotation around an arbitrary given axis, equivalent to estimating the phase of an arbitrary single-qubit quantum gate, both in noise-free and then in noisy conditions. In noise-free conditions, we establish the possibility of defining an optimal quantum probe, optimal quantum measurement, and optimal estimator together capable of achieving the ultimate best performance uniformly for any unknown phase. With arbitrary quantum noise, we show that in general the optimal solutions are phase dependent and require adaptive techniques for practical implementation. However, for the important case of the depolarizing noise, we again establish the possibility of a quantum probe, quantum measurement, and estimator uniformly optimal for any unknown phase. In this way, for qubit phase estimation, without and then with quantum noise, we characterize the phase-independent optimal solutions when they generally exist, and also identify the complementary conditions where the optimal solutions are phase dependent and only adaptively implementable.

We consider a narrow magneto-dipole transition in the ${}^{169}\text{Tm}$ atom at the wavelength of $1.14 \mu \mathrm{m}$ as a candidate for a two-dimensional-optical lattice clock. Calculating dynamic polarizabilities of the two clock levels $\left[\text{Xe}\right]4f^{13}6s^2(J=7/2)$ and $\left[\text{Xe}\right]4f^{13}6s^2(J=5/2)$ in the spectral range from 250 to 1200 nm, we find a “magic” wavelength for the optical lattice at 807 nm. Frequency shifts due to black-body radiation (BBR), the van der Waals interaction, the magnetic dipole-dipole interaction, and other effects which can perturb the transition frequency are calculated. The transition at $1.14 \mu \mathrm{m}$ demonstrates low sensitivity to the BBR shift corresponding to $8\times {10}^{-17}$ in fractional units at room temperature which makes it an interesting candidate for high-performance optical clocks. The total estimated frequency uncertainty is less than $5\times {10}^{-18}$ in fractional units. By direct excitation of the $1.14 \mu \mathrm{m}$ transition in Tm atoms loaded into an optical dipole trap, we set the lower limit for the lifetime of the upper clock level $\left[\text{Xe}\right]4f^{13}6s^2(J=5/2)$ of 112 ms which corresponds to a natural spectral linewidth narrower than 1.4 Hz. The polarizability of the Tm ground state was measured by the excitation of parametric resonances in the optical dipole trap at 532 nm.

We theoretically investigate the electron dynamics in Ne atoms involving core-excited states through the Ramsey scheme with a pair of time-delayed x-ray pulses. Irradiation of Ne atoms by the $\sim 1$ femtosecond x-ray pulse simultaneously populates two core-excited states, and an identical but time-delayed x-ray pulse probes the dynamics of the core-excited electron wave packet which is subject to the resonant Auger decay. The energy-integrated total Auger electron yield and energy-resolved Auger electron spectra in the time domain show periodic structures due to the temporal evolution of the wave packet, from which we can obtain the counterpart in the frequency domain through the Fourier transformation. The Auger electron energy spectra in the time as well as frequency domains show the interference patterns between the two Auger electron wave packets released into the continuum from the superposition of two core-excited states at different times. These spectra are important to clarify the individual contribution of the different Auger decay channels upon core excitation by the x-ray pulse.

Motivated by recent experiments, we study theoretically the dynamics of vortices in the crossover from two dimensions to one in atomic condensates in elongated traps. We explore the transition from the dynamics of a vortex to that of a dark soliton as the one-dimensional limit is approached, mapping this transition out as a function of the key system parameters. Moreover, we probe this transition dynamically through the hysteresis under time-dependent deformation of the trap at the dimensionality crossover. When the solitonic regime is probed during the hysteresis, significant angular momentum is lost from the system, but remarkably, the vortex can reemerge.

We study the spontaneous formation of defects in the order parameter of a trapped ultracold bosonic gas while crossing the critical temperature for Bose-Einstein condensation at different rates. The system has the shape of an elongated ellipsoid, whose transverse width can be varied. For slow enough temperature quenches we find a power-law scaling of the average defect number with the quench rate, as predicted by the Kibble-Zurek mechanism. A breakdown of such a scaling is found for fast quenches, leading to a saturation of the average defect number. We suggest an explanation for this saturation in terms of the mutual interactions among defects.

We theoretically show that the dipole force of an ensemble of quantum emitters embedded in a dielectric nanosphere can be exploited to achieve near-field optical levitation. The key ingredient is that the polarizability from the ensemble of embedded quantum emitters can be larger than the bulk polarizability of the sphere, thereby enabling the use of repulsive optical potentials and consequently the levitation using optical near fields. In levitated cavity quantum optomechanics, this could be used to boost the single-photon coupling by combining larger polarizability to mass ratio, larger field gradients, and smaller cavity volumes while remaining in the resolved sideband regime and at room temperature. A case study is done with a nanodiamond containing a high density of silicon-vacancy color centers that is optically levitated in the evanescent field of a tapered nanofiber and coupled to a high-finesse microsphere cavity.

We study the emergence of a collective optical response of a cold and dense ${}^{87}\mathrm{Rb}$ atomic cloud to a near-resonant low-intensity light when the atom number is gradually increased. Experimental observations are compared with microscopic stochastic simulations of recurrent scattering processes between the atoms that incorporate the atomic multilevel structure and the optical measurement setup. We analyze the optical response of an inhomogeneously broadened gas and find that the experimental observations of the resonance line shifts and the total collected scattered light intensity in cold atom clouds substantially deviate from those of thermal atomic ensembles, indicating strong light-induced resonant dipole-dipole interactions between the atoms. At high densities, the simulations also predict a significantly slower decay of light-induced excitations in cold than in thermal atom clouds. The role of dipole-dipole interactions is discussed in terms of resonant coupling examples and the collective radiative excitation eigenmodes of the system.

The possibility of focusing light to an ever tighter spot has important implications for many applications and fields of optics research, such as nano-optics and plasmonics, laser-scanning microscopy, optical data storage, and many more. The size of lateral features of the field at the focus depends on several parameters, including the numerical aperture of the focusing system, but also the wavelength and polarization, phase and intensity distribution of the input beam. Here, we study the smallest achievable focal feature sizes of coherent superpositions of two copropagating beams carrying opposite orbital angular momentum. We investigate the feature sizes for this class of beams not only in the scalar limit, but also use a fully vectorial treatment to discuss the case of tight focusing. Both our numerical simulations and our experimental results confirm that lateral feature sizes considerably smaller than those of a tightly focused Gaussian light beam can be observed. These findings may pave the way for improving the resolution of imaging systems or may find applications in nano-optics experiments.

The boundary between classical and quantum correlations is well characterized by linear constraints called Bell inequalities. It is much harder to characterize the boundary of the quantum set itself in the space of no-signaling correlations. For the points on the quantum boundary that violate maximally some Bell inequalities, J. Oppenheim and S. Wehner [Science 330, 1072 (2010)] pointed out a complex property: Alice's optimal measurements steer Bob's local state to the eigenstate of an effective operator corresponding to its maximal eigenvalue. This effective operator is the linear combination of Bob's local operators induced by the coefficients of the Bell inequality, and it can be interpreted as defining a fine-grained uncertainty relation. It is natural to ask whether the same property holds for other points on the quantum boundary, using the Bell expression that defines the tangent hyperplane at each point. We prove that this is indeed the case for a large set of points, including some that were believed to provide counterexamples. The price to pay is to acknowledge that the Oppenheim-Wehner criterion does not respect equivalence under the no-signaling constraint: for each point, one has to look for specific forms of writing the Bell expressions.

We investigate non-Hermitian Kitaev chains in which imaginary potentials are added to all or only the two end lattice sites to represent the physical gain and loss during their interacting processes with the environment. By analyzing the energy eigenvalues of the non-Hermitian Hamiltonians both analytically and numerically, we find that if the imaginary potentials are added to every lattice site, the topologically nontrivial phase region will be gradually narrowed down as the imaginary potentials increase. The zero-energy modes in the nontrivial phase region remain real and thus the Majorana bound states (MBSs) at the ends of the chain are presenting steadily until the imaginary potentials become strong enough to close the energy gap and change the bulk properties. However, if the imaginary potentials are only added to the two ends of the chain, the zero-energy modes will always be real and thus the MBSs exist stably all the time even when the imaginary potentials become very strong since the corresponding bulk properties cannot be changed by these two local perturbations. Our results explicitly demonstrate the evolution and robustness of the nontrivial topological state of Kitaev chain against external perturbations.

Digital signatures play an important role in software distribution, modern communication, and financial transactions, where it is important to detect forgery and tampering. Signatures are a cryptographic technique for validating the authenticity and integrity of messages, software, or digital documents. The security of currently used classical schemes relies on computational assumptions. Quantum digital signatures (QDS), on the other hand, provide information-theoretic security based on the laws of quantum physics. Recent work on QDS Amiri et al., Phys. Rev. A 93, 032325 (2016); Yin, Fu, and Zeng-Bing, Phys. Rev. A 93, 032316 (2016) shows that such schemes do not require trusted quantum channels and are unconditionally secure against general coherent attacks. However, in practical QDS, just as in quantum key distribution (QKD), the detectors can be subjected to side-channel attacks, which can make the actual implementations insecure. Motivated by the idea of measurement-device-independent quantum key distribution (MDI-QKD), we present a measurement-device-independent QDS (MDI-QDS) scheme, which is secure against all detector side-channel attacks. Based on the rapid development of practical MDI-QKD, our MDI-QDS protocol could also be experimentally implemented, since it requires a similar experimental setup.

In this paper, we use the nonlinear generator of dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with a precision above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the dependence of the state of the resonator on the unknown phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly efficient single photon detectors, it should be of practical interest until highly entangled many-photon states become more readily available.

Binary quantum information can be fault-tolerantly encoded in states defined in infinite-dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular variables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.

We investigate the effect of variations in beam-splitter transmissions and path-length differences in the nonlinear sign gate that is used for linear optical quantum computing. We identify two implementations of the gate and show that the sensitivity to variations in their components differs significantly between them. Therefore, circuits that require a precision implementation will generally benefit from additional circuit analysis of component variations to identify the most practical implementation. We suggest possible routes to efficient circuit analysis in terms of quantum parameter estimation.

Quantum annealing aims to exploit quantum mechanics to speed up the search for the solution to optimization problems. Most problems exhibit complete connectivity between the logical spin variables after they are mapped to the Ising spin Hamiltonian of quantum annealing. To account for hardware constraints of current and future physical quantum annealers, methods enabling the embedding of fully connected graphs of logical spins into a constant-degree graph of physical spins are therefore essential. Here, we compare the recently proposed embedding scheme for quantum annealing with all-to-all connectivity by Lechner, Hauke, and Zoller (LHZ) [Sci. Adv. 1, e1500838 (2015)] to the commonly used minor embedding (ME) scheme. Using both simulated quantum annealing and parallel tempering simulations, we find that for a set of instances randomly chosen from a class of fully connected, random Ising problems, the ME scheme outperforms the LHZ scheme when using identical simulation parameters, despite the fault tolerance of the latter to weakly correlated spin-flip noise. This result persists even after we introduce several decoding strategies for the LHZ scheme, including a minimum-weight decoding algorithm that results in substantially improved performance over the original LHZ scheme. We explain the better performance of the ME scheme in terms of more efficient spin updates, which allows it to better tolerate the correlated spin-flip errors that arise in our model of quantum annealing. Our results leave open the question of whether the performance of the two embedding schemes can be improved using scheme-specific parameters and new error correction approaches.

We report the development of quantum microscopic theory of quasiresonant dipole-dipole interaction in the ensembles of impurity atoms imbedded into transparent dielectric and located in a Fabry-Perot cavity. On the basis of the general approach we study the simultaneous influence of the cavity and resonant dipole-dipole interaction on the shape of the line of atomic transition as well as on light trapping in dense impurity ensembles. We analyze this influence depending on the size of the ensemble, its density, as well as on rms deviation of the transition frequency shifts caused by the symmetry disturbance of the internal fields of the dielectric medium. Obtained results are compared with the case when the cavity is absent. We show that the cavity can essentially modify cooperative polyatomic effects.

The energy and time-of-flight distributions of water ionic fragments produced by impact of fast atoms and bare and dressed ions; namely, ${\mathrm{H}}^{+}, {\mathrm{Li}}^{0–3+}, {\mathrm{C}}^{1+}$, and ${\mathrm{C}}^{2+}$ are reported in this work. Fragment species as a function of emission energy and time-of-flight were recorded by using an electrostatic spectrometer and a time-of-flight mass spectrometer, respectively. An improved Coulomb explosion model coupled to a classical trajectory Monte Carlo (CTMC) simulation gave the energy centroids of the fragments for the dissociation channels resulting from the removal of two to five electrons from the water molecule. For the energy distribution ranging up to 50 eV, both the experiment and model reveal an isotropic production of multiple charged oxygen ions, as well as hydrogen ions. From the ion energy distribution, relative yields of the dissociation resulting from multiple ionization were obtained as a function of the charge state, as well as for several projectile energies. Multiple-ionization yields with charge state up to 4+, were extracted from the measurements of the time-of-flight spectra, focused on the production of single and multiple charged oxygen ions. The measurements were compared to ion-water collision experiments investigated at the keV energy range available in the literature, revealing differences and similarities in the fragment-ion energy distribution.

We present theoretical photoelectron momentum distributions (PMDs) for ionization from Ar($3p$) and ${\mathrm{H}}_2{}^{+}$(${\sigma }_g$) orbitals by few-cycle, high-intensity, near-infrared laser fields circularly polarized in the $xy$ plane. The three-dimensional time-dependent Schrödinger equation is solved numerically within the single-active-electron approximation for Ar and within the fixed nuclei approximation for ${\mathrm{H}}_2{}^{+}$. The PMDs are investigated for alignment of the probed target orbitals relative to the polarization plane of the laser field. In the atomic case, the PMDs in the polarization plane for aligned $3p$ Ar orbitals are, up to an overall scaling factor, insensitive to alignment of the probed orbital, while the lateral PMDs show a signature of the orbital node when that node is sufficiently close to the polarization plane. For the molecular case of ${\mathrm{H}}_2{}^{+}$(${\sigma }_g$), our results show a significant impact of alignment on the PMDs due to the anisotropic molecular potential and the alignment-dependent coupling between the ground state and excited states.