Devil's crevasse and macroscopic entanglement in two-component Bose-Einstein condensates

Spin coherent states are the matter equivalent of optical coherent states, where a large number of two component particles form a macroscopic state displaying quantum coherence. Here we give a detailed study of entanglement generated between two spin-1/2 BECs due to an Sz1 Sz2 interaction. The states that are generated show a remarkably rich structure showing fractal characteristics. In the limit of large particle number N, the entanglement shows a strong dependence upon whether the entangling gate times are a rational or irrational multiple of pi/4. We discuss the robustness of various states under decoherence and show that despite the large number of particles in a typical BEC, entanglement on a macroscopic scale should be observable as long as the gate times are less than hbar/J sqrt[N], where J is the effective BEC-BEC coupling energy. Such states are anticipated to be useful for various quantum information applications such as quantum teleportation and quantum algorithms

Time dynamics of Bethe ansatz solvable models

We develop a method for finding the time evolution of exactly solvable models by Bethe ansatz. The dynamical Bethe wavefunction takes the same form as the stationary Bethe wavefunction except for time varying Bethe parameters and a complex phase prefactor. From this, we derive a set of first order nonlinear coupled differential equations for the Bethe parameters, called the dynamical Bethe equations. We find that this gives the exact solution to particular types of exactly solvable models, including the Bose-Hubbard dimer and Tavis-Cummings model. These models go beyond the Gaudin class, and offers an interesting possibility for performing time evolution in exactly solvable models.Comment: 9 pages, 1 figur

Skyrmion quantum spin Hall effect

The quantum spin Hall effect is conventionally thought to require a strong spin-orbit coupling, producing an effective spin-dependent magnetic field. However, spin currents can also be present without transport of spins, for example, in spin-waves or skyrmions. In this paper, we show that topological skyrmionic spin textures can be used to realize a quantum spin Hall effect. From basic arguments relating to the single-valuedness of the wave function, we deduce that loop integrals of the derivative of the Hamiltonian must have a spectrum that is integer multiples of $2 \pi$. By relating this to the spin current, we form a new quantity called the quantized spin current which obeys a precise quantization rule. This allows us to derive a quantum spin Hall effect, which we illustrate with an example of a spin-1 Bose-Einstein condensate.Comment: 7 pages, 2 figures (published in PRB

Light mediated non-Gaussian atomic ensemble entanglement

We analyze a similar scheme for producing light-mediated entanglement between atomic ensembles, as first realized by Julsgaard, Kozhekin and Polzik [Nature {\bf 413}, 400 (2001)]. In the standard approach to modeling the scheme, a Holstein-Primakoff approximation is made, where the atomic ensembles are treated as bosonic modes, and is only valid for short interaction times. In this paper, we solve the time evolution without this approximation, which extends the region of validity of the interaction time. For short entangling times, we find this produces a state with similar characteristics as a two-mode squeezed state, in agreement with standard predictions. For long entangling times, the state evolves into a non-Gaussian form, and the two-mode squeezed state characteristics start to diminish. This is attributed to more exotic types of entangled states being generated. We characterize the states by examining the Fock state probability distributions, Husimi $Q$ distributions, and non-local entanglement between the ensembles. We compare and connect several quantities obtained using the Holstein-Primakoff approach and our exact time evolution methods

Entanglement generation in quantum networks of Bose-Einstein condensates

Two component (spinor) Bose-Einstein condensates (BECs) are considered as the nodes of an interconnected quantum network. Unlike standard single-system qubits, in a BEC the quantum information is duplicated in a large number of identical bosonic particles, thus can be considered to be a "macroscopic" qubit. One of the difficulties with such a system is how to effectively interact such qubits together in order to transfer quantum information and create entanglement. Here we propose a scheme of cavities containing spinor BECs coupled by optical fiber in order to achieve this task. We discuss entanglement generation and quantum state transfer between nodes using such macroscopic BEC qubits.Comment: 17 pages, 4 figure

Suppression of ac Stark shift scattering rate due to non-Markovian behavior

The ac Stark shift in the presence of spontaneous decay is typically considered to induce an effective dephasing with a scattering rate equal to $\Gamma_s |\Omega|^2/\Delta^2$, where $\Gamma_s$ is the spontaneous decay rate, $\Omega$ is the laser transition coupling, and $\Delta$ is the detuning. We show that under realistic circumstances this dephasing rate may be strongly modifed due to non-Markovian behavior. The non-Markovian behavior arises due to an effective modification of the light-atom coupling in the presence of the ac Stark shift laser. An analytical formula for the non-Markovian ac Stark shift induced dephasing is derived. We obtain that for narrow laser linewidths the effective dephasing rate is suppressed by a factor of $Q^2$, where $Q$ is the quality factor of the laser.Comment: Accepted in PRA Rapid Communication

Landau-Zener transition stabilized by the enhanced quantum Zeno effect in the bosonic system

We study the Landau-Zener transition with the quantum Zeno effect in an open dissipative system populated by a large number of bosons. Given the quantum Zeno effect is strong enough, both discrete and continuous quantum Zeno measurements are found to stabilize the Landau-Zener transition. Both the $\sigma^x$-type longitudinal relaxation and $\sigma^z$-type transverse relaxation in the bosonic system are analyzed as a model of continuous quantum Zeno measurements. While both of them improve the signal-to-noise ratio in terms of the ground state population, the $\sigma^x$-type relaxation can further boost measurement sensitivity and thus lead to a polynomial speedup with the number of bosons in the system. For a system that contains a large number of bosons such as in a Bose-Einstein condensate with more than $10^4$ bosons, this equates to several orders of magnitude speedup.Comment: 9 pages, 3 figure

Optimization using Bose-Einstein condensation and measurement-feedback circuits

We investigate a computational device that harnesses the effects of Bose-Einstein condensation (BEC) to accelerate the speed of finding the solution of a given optimization problem. Many computationally difficult problems, including NP-complete problems, can be formulated as a ground state search problem. In a BEC, below the critical temperature, bosonic particles have a natural tendency to accumulate in the ground state. Furthermore, the speed of attaining this configuration is enhanced as a result of final state stimulation. We propose a physical device that incorporates these basic properties of bosons into the optimization problem, such that an optimized solution is found by a simple cooling of the physical temperature of the device. We find that the speed of convergence to the ground state can be sped up by a factor of $N$ at a given error, where N is the boson number per site.Comment: 10 pages, 3 figure

Covariance matrix entanglement criterion for an arbitrary set of operators

We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by performing a partial transposition on the operators. The method is highly efficient and versatile in the sense that the set of measurement operators can be freely chosen, do not need to be complete, and there is no constraint on the commutation relations. The method is particularly suited for systems with higher dimensionality since the computations do not scale with the dimension of the Hilbert space rather they scale with the number of chosen observables which can always be kept small. We illustrate the approach by examining the entanglement between two spin ensembles, and show that it detects entanglement in a basis independent way

Quantum coherence of planar spin models with Dzyaloshinsky-Moriya interaction

The quantum coherence of one dimensional planar spin models with the Dzyaloshinsky-Moriya interaction is investigated. The anisotropic XY model, the isotropic XX model and the transverse field model are studied in the large N-limit using the two qubit reduced density matrices and the two point correlation functions. From our investigations we find that the coherence as measured using the Jensen-Shannon divergence can be used to detect the quantum phase transitions and the quantum critical points. The derivative of coherence shows non-analytic behavior at the critical points leading to the conclusions that these transitions are of second order. Further we show that the presence of the Dzyaloshinsky-Moriya coupling suppresses the phase transition due to the residual ferromagnetism which is caused by spin canting.Comment: accepted for publication in Physical Review