Spin Coherent States Research Articles

Quantum computation mediated by ancillary qudits and spin coherent states

Models of universal quantum computation in which the required interactions between register (computational) qubits are mediated by some ancillary system are highly relevant to experimental realizations of a quantum computer. We introduce such a universal model that employs a $d$-dimensional ancillary qudit. The ancilla-register interactions take the form of controlled displacements operators, with a displacement operator defined on the periodic and discrete lattice phase space of a qudit. We show that these interactions can implement controlled phase gates on the register by utilizing geometric phases that are created when closed loops are traversed in this phase space. The extra degrees of freedom of the ancilla can be harnessed to reduce the number of operations required for certain gate sequences. In particular, we see that the computational advantages of the quantum bus (qubus) architecture, which employs a field-mode ancilla, are also applicable to this model. We then explore an alternative ancilla-mediated model which employs a spin ensemble as the ancillary system and again the interactions with the register qubits are via controlled displacement operators, with a displacement operator defined on the Bloch sphere phase space of the spin coherent states of the ensemble. We discuss the computational advantages of this model and its relationship with the qubus architecture.

Precision measurements using squeezed spin states via two-axis countertwisting interactions

We show that the two-axis counter twisting interaction squeezes a coherent spin state into three states of interest in quantum information, namely, the twin-Fock state, the equally-weighted superposition state, and the state that achieves the Heisenberg limit of optimal sensitivity defined by the Cramer-Rao inequality in addition to the well-known Heisenberg-limited state of spin fluctuations.

Full-Bloch-sphere teleportation of spinor Bose-Einstein condensates and spin ensembles

Quantum teleportation is the transfer of quantum information between two locations by the use of shared entanglement. Current teleportation schemes broadly fall under one of two categories, either qubit or continuous-variable teleportation. Spin coherent states on spin ensembles can be teleported under the continuous-variable approximation for states with small deviations from a given polarization. However, for spin-coherent states with large deviations, no convenient teleportation protocol exists. Recently, we introduced a teleportation scheme where a spin-coherent state lying on the equator of the Bloch sphere is teleported between distant parties [A. N. Pyrkov and T. Byrnes, New J. Phys. 16, 073038 (2014)]. Here we generalize the protocol to a spin-coherent state with an arbitrary position on the Bloch sphere. Our proposed scheme breaks classical bounds based on communication in the unconditional case and quantum state estimation with postselection.

M-Flip Concurrence in the Framework of Multipartite Spin Coherent States

M-Flip Concurrence in the Framework of Multipartite Spin Coherent States

Single-shot quantum state estimation via a continuous measurement in the strong backaction regime

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here the case in which the measurement-induced backaction has a nonnegligible effect on the dynamical evolution of the ensemble. We formulate a maximum likelihood estimate for the initial quantum state given only a single instance of the continuous diffusive measurement record. We apply our estimator to the simplest problem -- state tomography of a single pure qubit, which, during the course of the measurement, is also subjected to dynamical control. We identify a regime where the many-body system is well approximated at all times by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochastic evolution. We simulate the results of our estimator and show that we can achieve close to the upper bound of fidelity set by the optimal POVM. This estimate is compared to, and significantly outperforms, an equivalent estimator that ignores measurement backaction.

Proposal for the creation and optical detection of spin cat states in Bose-Einstein condensates.

We propose a method to create "spin cat states," i.e., macroscopic superpositions of coherent spin states, in Bose-Einstein condensates using the Kerr nonlinearity due to atomic collisions. Based on a detailed study of atom loss, we conclude that cat sizes of hundreds of atoms should be realistic. The existence of the spin cat states can be demonstrated by optical readout. Our analysis also includes the effects of higher-order nonlinearities, atom number fluctuations, and limited readout efficiency.

Macroscopic quantum information processing using spin coherent states

Previously a new scheme of quantum information processing based on spin coherent states of two component Bose–Einstein condensates was proposed (Byrnes et al. Phys. Rev. A 85, 40306(R)). In this paper we give a more detailed exposition of the scheme, expanding on several aspects that were not discussed in full previously. The basic concept of the scheme is that spin coherent states are used instead of qubits to encode qubit information, and manipulated using collective spin operators. The scheme goes beyond the continuous variable regime such that the full space of the Bloch sphere is used. We construct a general framework for quantum algorithms to be executed using multiple spin coherent states, which are individually controlled. We illustrate the scheme by applications to quantum information protocols, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.

Quantum and Classical Correlations in the Solid-State NMR Free Induction Decay

The free induction decay (FID) of the transverse magnetization in a dipolar-coupled rigid lattice is a fundamental problem in magnetic resonance and in the theory of many-body systems. As it was shown earlier the FID shapes for the systems of classical magnetic moments and for quantum nuclear spin ones coincide if there are many nearly equivalent nearest neighbors n in a solid lattice. In this paper, we reduce a multispin density matrix of above system to a two-spin matrix. Then we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations at the arbitrary spin quantum number S, in the high-temperature approximation. The time dependence of these functions is expressed via the derivative of the FID shape. To extract classical correlations for S > 1/2 we provide generalized POVM measurement (positive-operator-valued measure) using the basis of spin coherent states. We show that in every pair of spins the portion of quantum correlations changes from 1/2 to 1/(S + 1) when S is growing up, and quantum properties disappear completely only if S → ∞.

Transformation of Ramsey electromagnetically induced absorption into magnetic-field induced transparency in a paraffin-coated Rb vapor cell

We report on magnetic-field induced transparency (MIT) based on Ramsey electromagnetically induced absorption (EIA) in a paraffin-coated Rb vapor cell. Changing the laser polarization from linear to circular in the presence of a weak residual transverse magnetic field to the laser propagation, the narrow absorption due to the Ramsey EIA transformed into the transparency due to MIT of the 5S1/2 (F = 2)-5P3/2 (F' = 3) transition of 87Rb in the paraffin-coated Rb vapor cell. The spectral widths of the EIA and MIT in the Hanle configuration were measured to be 0.6 mG (425 Hz) and 1.2 mG, respectively. MIT depended on the long preservation time of the ground-state coherent spin states and the transverse magnetic field. From the numerical results, the crossover between the Ramsey EIA and the MIT could be illustrated as the superposition of both signals.

Fractional revivals, multiple-Schrödinger-cat states, and quantum carpets in the interaction of a qubit withNqubits

We study the dynamics of a system comprised of a single qubit interacting equally with $N$ qubits (a ``spin star'' system). Although this model can be solved exactly, the exact solution does not give much intuition for the dynamics of the model. Here, we find an approximation that gives some insight into the dynamics for a particular class of initial spin-coherent states of the $N$ qubits. We find an effective Hamiltonian for the system that is a finite Kerr (one-axis twisting) Hamiltonian for the $N+1$ qubits. The initial spin-coherent state evolves to spin-squeezed states on short time scales, and to ``multiple-Schr\"odinger-cat'' states (superpositions of many spin-coherent states) on longer time scales, a manifestation of the phenomenon of fractional revivals of the initial state. The evolution of the system is visualized with phase-space plots ($Q$ functions) that, when plotted against time, reveal a ``quantum carpet'' pattern. Of particular interest is the fact that our approximation captures the qualitative features of the model even for small values of $N$. This suggests the possibility of observing the phenomenon of fractional revival in this model for systems of few qubits.

Generating non-classical states from spin coherent states via interaction with ancillary spins

The generation of non-classical states of large quantum systems has attracted much interest from a foundational perspective, but also because of the significant potential of such states in emerging quantum technologies. In this paper we consider the possibility of generating non-classical states of a system of spins by interaction with an ancillary system, starting from an easily prepared initial state. We extend previous results for an ancillary system comprising a single spin to bigger ancillary systems and the interaction strength is enhanced by a factor of the number of ancillary spins. Depending on initial conditions, we find – by a combination of approximation and numerics – that the system of spins can evolve to spin cat states, spin squeezed states or to multiple cat states. We also discuss some candidate systems for implementation of the Hamiltonian necessary to generate these non-classical states.

Quantum teleportation of spin coherent states: beyond continuous variables teleportation

We introduce a quantum teleportation scheme that transfers a spin coherent state between two locations using entanglement. In the scheme an unknown spin coherent state lying on the equator of the Bloch sphere, such as realized in a coherent two-component Bose–Einstein condensate, is teleported onto a distant spin coherent state using only elementary operations and measurements. The scheme works in the regime beyond the standard continuous variables approximation based on the Holstein–Primakoff transformation. We analyze the error of the protocol with the number of particles N in the spin coherent state under decoherence and find that it scales favorably with N. The simplicity of the operations involved and the robustness under decoherence should make the protocol suitable under realistic experimental conditions.

Coherence and squeezing in Z3‐graded spin coherent states

AbstractA new kind of spin coherent state called a Z3‐graded spin coherent state is constructed by using the complex solution of the equation q3 = 1. We explicitly find three kinds of Z3‐graded spin coherent states. The associated coherent property and spin squeezing are also examined.

Feedback control of coherent spin states using weak nondestructive measurements

We consider the decoherence of a pseudospin ensemble under collective random rotations and study, both theoretically and experimentally, how a nondestructive measurement combined with real-time feedback correction can protect the state against such a decoherence process. We theoretically characterize the feedback efficiency with different parameters---coherence, entropy, fidelity---and show that a maximum efficiency is reached in the weak measurement regime, when the projection of the state induced by the measurement is negligible. This article presents in detail the experimental results published previously [T. Vanderbruggen et al., Phys. Rev. Lett. 110, 210503 (2013)], where the feedback scheme stabilizes coherent spin states of trapped ultracold atoms and nondestructively probes them with dispersive optical detection. In addition, we study the influence of several parameters, such as atom number and rotation angle, on the performance of the method. We analyze the various decoherence sources limiting the feedback efficiency and propose a way to mitigate their effect. The results demonstrate the potential of the method for the real-time coherent control of atom interferometers.

Rabi oscillations, decoherence, and disentanglement in a qubit–spin-bath system

We examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one-dimensional spin bath. In contrast to previous studies, both the qubit-bath coupling and the nearest neighbor intrabath couplings are taken as the spin-flip XX-type. We first study the Rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state, finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics. Next, we discuss the bath-induced decoherence of the qubit when the bath is initially in the ground state, and show that the decoherence properties depend on the internal phases of the spin bath. By considering two independent copies of the qubit-bath system, we finally probe the disentanglement dynamics of two noninteracting entangled qubits. We find that entanglement sudden death appears when the spin bath is in its critical phase. We show that the single-qubit decoherence factor is an upper bound for the two-qubit concurrence.

Evolution dynamics of a model for gene duplication under adaptive conflict.

We present and solve the dynamics of a model for gene duplication showing escape from adaptive conflict. We use a Crow-Kimura quasispecies model of evolution where the fitness landscape is a function of Hamming distances from two reference sequences, which are assumed to optimize two different gene functions, to describe the dynamics of a mixed population of individuals with single and double copies of a pleiotropic gene. The evolution equations are solved through a spin coherent state path integral, and we find two phases: one is an escape from an adaptive conflict phase, where each copy of a duplicated gene evolves toward subfunctionalization, and the other is a duplication loss of function phase, where one copy maintains its pleiotropic form and the other copy undergoes neutral mutation. The phase is determined by a competition between the fitness benefits of subfunctionalization and the greater mutational load associated with maintaining two gene copies. In the escape phase, we find a dynamics of an initial population of single gene sequences only which escape adaptive conflict through gene duplication and find that there are two time regimes: until a time t single gene sequences dominate, and after t double gene sequences outgrow single gene sequences. The time t is identified as the time necessary for subfunctionalization to evolve and spread throughout the double gene sequences, and we show that there is an optimum mutation rate which minimizes this time scale.

Cavity-aided nondemolition measurements for atom counting and spin squeezing

Probing the collective spin state of an ensemble of atoms may provide a means to reduce heating via the photon recoil associated with the measurement and provide a robust, scalable route for preparing highly entangled states with spectroscopic sensitivity below the standard quantum limit for coherent spin states. The collective probing relies on obtaining a very large optical depth that can be effectively increased by placing the ensemble within an optical cavity such that the probe light passes many times through the ensemble. Here we provide expressions for measurement resolution and spectroscopic enhancement in such cavity-aided non-demolition measurements as a function of cavity detuning. In particular, fundamental limits on spectroscopic enhancements in $^{87}$Rb are considered.

Quantum Fisher information and spin squeezing in one-axis twisting model

We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ0, φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 (2009) 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near-Heisenberg limit ∝ 2/N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0 ∼ π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.

Optical continuous-variable quadratic phase gate via Faraday interaction

The continuous-variable (CV) quadratic phase gate is one of the most fundamental CV quantum gates for universal CV quantum computation, while its experimental realization still remains a challenge. Here we propose a novel and experimentally feasible scheme to realize optical CV quadratic phase gate via Faraday interaction in an atomic ensemble. The gate is performed by simply sending an optical beam three times through an atomic medium prepared in coherent spin state. The fidelity of the gate can ideally run up to one. We show that the scheme also works well as a device to generate optical polarization squeezing. Considering the noise effects due to atomic decoherence and light losses, we find that the observed fidelities of gate operation and the attainable degree of polarization squeezing are still quite high.

Coherent all-optical control of ultracold atoms arrays in permanent magnetic traps

We propose a hybrid architecture for quantum information processing based on magnetically trapped ultracold atoms coupled via optical fields. The ultracold atoms, which can be either Bose-Einstein condensates or ensembles, are trapped in permanent magnetic traps and are placed in microcavities, connected by silica based waveguides on an atom chip structure. At each trapping center, the ultracold atoms form spin coherent states, serving as a quantum memory. An all-optical scheme is used to initialize, measure and perform a universal set of quantum gates on the single and two spin-coherent states where entanglement can be generated addressably between spatially separated trapped ultracold atoms. This allows for universal quantum operations on the spin coherent state quantum memories. We give detailed derivations of the composite cavity system mediated by a silica waveguide as well as the control scheme. Estimates for the necessary experimental conditions for a working hybrid device are given.