We investigate Zitterbewegung (ZB) of the ultracold atoms in a tunable honeycomb optical lattice. By tuning the parameters of the lattice one can realize the merging of two Dirac points. The process of two Dirac points merging into a hybrid point implies a topological phase transition from a semimetallic to a band insulator phase. After merging, it presents a linear-quadratic dispersion relation which is linear in one direction and quadric in the other orthogonal direction. We show that ZB occurs isotropically before merging but occurs only in the direction of the linear dispersion after merging. Furthermore, we obtain that ZB is exponentially damping for a negative energy gap but is a stable oscillation for a positive energy gap. The frequency and amplitude of ZB can be controlled in a detectable range, so the phenomena can be observable in the ultracold atomic experiments.

Electrically induced normal pressure and tangential stress at the surface of a small dielectric sphere (or cavity) in a dielectric are calculated using the Minkowski, Einstein-Laub, Abraham, and Lorentz forms of the Maxwell stress tensor. Only the Lorentz tensor is in agreement with the following observations: (1) A spherical cavity in a dielectric transforms into a sharp-edge plate perpendicular to the electric field; (2) a liquid drop placed in a medium with a slightly lower refractive index is stretched along the electric field; and (3) there is a torque on a small birefringent sphere. These phenomena cannot be explained by the conventional theory using the Minkowski stress tensor. For example, the Minkowski stress tensor predicts lateral compression of a spherical cavity in a dielectric.

Chirped biphotons generated via spontaneous parametric down-conversion in chirped quasi-phase-matched nonlinear crystals have ultrabroadband frequency spectra, while their correlation times are not ultranarrow, due to the nonlinear frequency dependence of the phase factor. Based on the idea of Fresnel zone lenses, we propose a Fresnel-inspired binary phase-shaping scheme for tailoring broadband biphoton spectra. By applying binary phase masks to the biphoton spectrum, a Fresnel zone lens was produced in the frequency domain, compressing the broadband temporal wave packets of the chirped biphotons to the Fourier-transform limit due to the effective removal of the quadratic phase. Furthermore, biphoton correlation trains can also be generated by properly shaping the biphoton spectrum with this scheme. This provides a method for biphoton compression and shaping, which avoids the length dependence and the impact of higher-order dispersion in a dispersive medium by using the phase compensation method. Our results could prove useful in quantum metrology, lithography, and coding of entangled photons.

A superconducting quantum interference device (SQUID) inserted in a superconducting waveguide resonator imposes current and voltage boundary conditions that makes it suitable as a tuning element for the resonator modes. If such a SQUID element is subject to a periodically varying magnetic flux, the resonator modes acquire frequency sidebands. In this work we calculate the multifrequency eigenmodes of resonators coupled to periodically driven SQUIDs and we use the Lagrange formalism to propose a theory for their quantization. The elementary excitations of a multifrequency mode can couple resonantly to physical systems with different transition frequencies and this makes the resonator an efficient quantum bus for state transfer and coherent quantum operations in hybrid quantum systems. As an example of the application of our multifrequency modes, we determine their coupling to transmon qubits with different frequencies and we present a bichromatic scheme for entanglement and gate operations.

Superconducting qubits, while promising for scalability and long coherence times, contain more than two energy levels, and therefore are susceptible to errors generated by the leakage of population outside of the computational subspace. Such leakage errors constitute a prominent roadblock towards fault-tolerant quantum computing (FTQC) with superconducting qubits. FTQC using topological codes is based on sequential measurements of multiqubit stabilizer operators. Here, we first propose a leakage-resilient procedure to perform repetitive measurements of multiqubit stabilizer operators, and then use this scheme as an ingredient to develop a leakage-resilient approach for surface code quantum error correction with superconducting circuits. Our protocol is based on swap operations between data and ancilla qubits at the end of every cycle, requiring read-out and reset operations on every physical qubit in the system, and thereby preventing persistent leakage errors from occurring.

We present methods and results for tomographic measurement of quantum systems through shot-by-shot correlation of individual qubit measurements. Rather than inferring the qubit state after each measurement, we show that averaging of continuous soft values is a valid tomographic strategy and is in fact the better choice in the regime of low signal-to-noise ratio. We experimentally demonstrate a matched filter approach to account for a transient measurement response, and use this to show that tomography of entangled states is feasible despite the asymptotic exponential effort required to obtain $N$-body corrleations.

Vast developments in quantum technology have enabled the preparation of quantum states with more than a dozen entangled qubits. The full characterization of such systems demands distinct constructions depending on their specific type and the purpose of their use. Here we present a method that scales linearly with the number of qubits for characterizing stabilizer states. Our approach allows simultaneous extraction of information about the fidelity, the entanglement, and the nonlocality of the state and thus is of high practical relevance. We demonstrate the efficient applicability of our method by performing an experimental characterization of a photonic four-qubit cluster state and three- and four-qubit Greenberger-Horne-Zeilinger states. Our scheme can be directly extended to larger-scale quantum information tasks.

We consider a hybrid three-mode optomechanical system where one mechanical oscillator couples to a second one via a Coulomb force and to a cavity mode via an optomechanical interaction. It is shown that stationary cavity-mechanical entanglement can be achieved by effectively cooling a Bogoliubov mode via the intermediate mode acting as an engineered reservoir. The entanglement can be maximized by carefully balancing the two confronting effects of the ratio of the effective couplings. Moreover, we analyze in detail the effects of the nonresonant terms. It is found that while the stability zone of the system shrinks in the parameter plane for large cooperativity, the maximal entanglement is not significantly reduced by the nonresonant terms. We numerically optimize the ratio in the stable region and obtain remarkably strong entanglement in the large cooperativity regime.

A significant problem for optical quantum computing is inefficient or inaccurate photodetectors. It is possible to use controlled-not (cnot) gates to improve a detector by making a large cat state, then measuring every qubit in that state. In this paper we develop a code that compares five different schemes for making multiple measurements, some of which are capable of detecting loss and some of which are not. We explore how each of these schemes performs in the presence of different errors, and derive a formula to find at what probability of qubit loss it is worth detecting loss, and at what probability does this just lead to further errors than the loss introduces.

A maximal steady-state fermionic entanglement of a nanoelectronic system is generated in finite temperature non-Markovian environments. The fermionic entanglement dynamics is presented by connecting the exact solution of the system with an appropriate definition of fermionic entanglement. We prove that the two understandings of the dissipationless non-Markovian dynamics, namely, the bound state and the modified Laplace transformation, are completely equivalent. For comparison, the steady-state entanglement is also studied in the wide-band limit and Born-Markovian approximation. When the environments have a finite band structure, we find that the system presents various kinds of relaxation processes. The final states can be thermal or thermal-like states, quantum memory states, and oscillating quantum memory states. Our study provides an analytical way to explore the non-Markovian entanglement dynamics of identical fermions in a realistic setting, i.e., finite-temperature reservoirs with a cutoff spectrum.

We propose an alternate pulse sequence for dynamical averaging of the dipole-dipole interactions and inhomogeneity of the magnetic fields in the nuclear-spin system. The sequence contains a short cycle of the periodic resonant pulse excitation that offers new possibilities for implementing the long-lived multiqubit quantum memory on the condensed spin ensembles that are so important for the construction of a universal quantum computer and long-distance quantum communications.

In this paper, we analyze the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under restricted local operation and classical communication. Based on this local distinguishability analysis, we propose a quantum secret sharing scheme (which we call LOCC-QSS). Our LOCC-QSS scheme is quite general and cost efficient compared to other schemes. In our scheme, no joint quantum operation is needed to reconstruct the secret. We also present an interesting $(2,n)$-threshold LOCC-QSS scheme, where any two cooperating players, one from each of two disjoint groups of players, can always reconstruct the secret. This LOCC-QSS scheme is quite uncommon, as most $(k,n)$-threshold quantum secret sharing schemes have the restriction $k\ge \lceil \frac{n}{2}\rceil$.

According to quantum mechanics, chiral molecules, that is, molecules that rotate the polarization of light, should not exist. The simplest molecules which can be chiral have four or more atoms with two arrangements of minimal potential energy that are equivalent up to a parity operation. Chiral molecules correspond to states localized in one potential energy minimum and can not be stationary states of the Schrödinger equation. A possible solution of the paradox can be founded on the idea of spontaneous symmetry breaking. This idea was behind work we did previously involving a localization phase transition: at low pressure, the molecules are delocalized between the two minima of the potential energy while at higher pressure they become localized in one minimum due to the intermolecular dipole-dipole interactions. Evidence for such a transition is provided by measurements of the inversion spectrum of ammonia and deuterated ammonia at different pressures. A previously proposed model gives a satisfactory account of the empirical results without free parameters. In this paper, we extend this model to gas mixtures. We find that also in these systems a phase transition takes place at a critical pressure which depends on the composition of the mixture. Moreover, we derive formulas giving the dependence of the inversion frequencies on the pressure. These predictions are susceptible to experimental test.

Formation of a secondary plasma of ${\mathrm{NO}}^{+}$ ions and electrons within an ultracold plasma produces an observable change in the hydrodynamics of the system. Direct photoionization adds energetic electrons, which increases the rate of expansion. The introduction of a secondary Rydberg gas has the opposite effect. In both cases, the added ions create an inertial drag that acts initially to retard the expansion of the electron gas. A cold-ion hydrodynamic shell model, which accounts well for the effect of energy added by photoionization electrons, predicts the formation of collisionless shock waves.

Tunneling and over-the-barrier ionization of alkali-metal atoms in strong electromagnetic fields are studied using the single-electron model (valence electron plus atomic core) and the frozen-core approximation. The lowest-state energies and widths (ionization rates) at different values of applied field, obtained using the Stark shift expansion and the Ammosov-Delone-Krainov formula, respectively, are compared with the corresponding values determined numerically by the complex rotation method. Good agreement for the energies is obtained at the field strengths corresponding to the tunneling regime. In contrast, the rates obtained by the Ammosov-Delone-Krainov formula significantly overestimate numerical results. After introducing a correction in the formula that accounts for the dependence of the binding energy on the field strength, good agreement in the tunneling regime is obtained for the rates too. A disagreement that still remains in the over-the-barrier ionization regime indicates that at stronger fields further corrections of the rate formula, such as those related to the form of the bound-state wave function, are required. Finally, it is demonstrated that numerically determined ionization rates are not too sensitive to the choice of model for the effective core potential and good results can be obtained using a simple local pseudopotential.

We investigate the ability of quantum optimal control theory to shape pulses suppressing strong-field ionization of a hydrogen atom and a ${\mathrm{H}}_2{}^{+}$ molecule. We show that considerable suppression of the ionization yield can be achieved for both H and ${\mathrm{H}}_2{}^{+}$ with optimal pulse shaping for a fixed fluence and pulse length. The mechanisms responsible for ionization suppression and the shape of the optimized pulse are different for infrared and ultraviolet laser fields. In the low-frequency regime the optimized pulse reduces the ionization yield by suppressing the highest peaks of the laser field. For the higher laser frequencies considered the ionization yield of H can be decreased by exciting low-lying resonances.

In the present contribution, we explore a host of different stationary states, namely dark-bright solitons and their lattices, that arise in the context of multicomponent atomic Bose-Einstein condensates. The latter are modeled by systems of coupled Gross-Pitaevskii equations with general interaction (nonlinearity) coefficients $g_{ij}$. It is found that in some particular parameter ranges such solutions can be obtained in analytical form, however, numerically they are computed as existing in a far wider parametric range. Many features of the solutions under study, such as their analytical form without the trap or the stability and dynamical properties of one dark-bright soliton even in the presence of the trap are obtained analytically and corroborated numerically. Additional features, such as the stability of soliton lattice homogeneous states or their existence and stability in the presence of the trap, are examined numerically.

We consider a one-dimensional gas of cold atoms with strong contact interactions and construct an effective spin-chain Hamiltonian for a two-component system. The resulting Heisenberg spin model can be engineered by manipulating the shape of the external confining potential of the atomic gas. We find that bosonic atoms offer more flexibility for independently tuning the parameters of the spin Hamiltonian through interatomic (intraspecies) interaction, which is absent for fermions due to the Pauli exclusion principle. Our formalism can have important implications for control and manipulation of the dynamics of few- and many-body quantum systems; as an illustrative example relevant to quantum computation and communication, we consider state transfer in the simplest nontrivial system of four particles representing exchange-coupled qubits.

We propose a simple realistic two-dimensional complex parity-time-symmetric photonic structure that is described by a non-Hermitian potential but possesses real-valued eigenvalues. The concept is developed from basic physical considerations to provide asymmetric coupling between harmonic wave components of the electromagnetic field. The structure results in a nonreciprocal chirality and asymmetric transmission between in- and out-coupling channels into the structure. The analytical results are supported by a numerical study of the Bloch-like mode formations and calculations of a realistic planar semiconductor structure.

The Floquet eigenvalue problem is analyzed for periodically driven Friedrichs models on discrete and continuous space. In the high-frequency regime, there exists a Floquet bound state consistent with the Floquet-Magnus expansion in the discrete Friedrichs model, while it is not the case in the continuous model. In the latter case, however, the bound state predicted by the Floquet-Magnus expansion appears as a metastable state whose lifetime diverges in the limit of large frequencies. We obtain the lifetime by evaluating the imaginary part of the quasienergy of the Floquet resonant state. In the low-frequency regime, there is no Floquet bound state and instead the Floquet resonant state with exponentially small imaginary part of the quasienergy appears, which is understood as the quantum tunneling in the energy space.