We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator with time as well as a phase decoherence of the component states.
Numerical calculations to examine the time evolution of GHZ state generation probability and population inversion for different system environment coupling strengths are performed. Using negativity as an entanglement measure and linear entropy as a measure of mixedness, the entanglement dynamics of the tripartite system in the presence of decoherence is analysed.
We analyse the effects of intrinsic decoherence on the probability of generating a tripartite GHZ state using a cool trapped ion coupled to a single mode of the cavity field and interacting with a resonant laser field. Milburn equation is solved for this tripartite system to obtain the time evolution of density matrix as a function of cavity-ion coupling, laser-ion coupling, and the size of unitary time step relative to the time scale determined by system parameters. Starting with the system prepared initially in a separable state, density matrix is used to calculate the probability of tripart…
In the present paper, we study spin squeezing under decoherence in the superposition of tripartite maximally entangled GHZ and W states. Here we use amplitude damping, phase damping and depolarisation channel. We have investigated the dynamics of spin squeezing with the interplay of superposition and decoherence parameters with different directions of the mean spin vector. We have found the mixture of GHZ and W states is robust against spin squeezing generation for amplitude damping and phase damping channels for certain directions of the mean spin vector. However, the depolarisation channel p…
We present a single step scheme to generate, experimentally, maximally entangled tripartite GHZ state in a single ion, using trapped ion interacting simultaneously with a resonant external laser field and red sideband tuned quantized cavity field. Besides the simplicity of execution and short operation time, GHZ state generation is reduction free. Pacs: 03.67.-a, 42.50.-p, 03.67.Dd
An array of ultracold polar molecules trapped in an external electric field is regarded as a promising carrier of quantum information. Under the action of this field, molecules are compelled to undergo pendular oscillations by the Stark effect. Particular attention has been paid to the influence of intrinsic decoherence on the model of linear polar molecular pendular states, thereby we evaluate the tripartite entanglement with negativity, as well as fidelity of bipartite quantum systems for input and output signals using electric dipole moments of polar molecules as qubits. According to this s…
The one-tangle and π-tangle are used to quantify the entanglement of a tripartite GHZ state in noninertial frames when the system interacts with a noisy environment in the form of phase damping, phase flip and bit flip channel. It is shown that the two-tangles behave as a closed system. The one-tangle and π-tangle have different behaviors in the three channel. In the case of phase damping channel, depending on the kind of coupling, the sudden death of both one-tangle and π-tangle may or may not happen. Whereas in the case of phase flip channel the sudden death cannot be avoided. The effect of …
We present a fully analytical solution of the dynamics of two strongly-driven atoms resonantly coupled to a dissipative cavity field mode. We show that an initial atom-atom entanglement cannot be increased. In fact, the atomic Hilbert space divides into two subspaces, one of which is decoherence free so that the initial atomic entanglement remains available for applications, even in presence of a low enough atomic decay rate. In the other subspace a measure of entanglement, decoherence, and also purity, are described by a similar functional behavior that can be monitored by joint atomic measur…
Evolution of tripartite entanglement in three-qubit Quantum Gravity-Induced Entanglement of Masses (QGEM) with quantum decoherence
Instituto de Física Teórica, UAM-CSIC（理论物理研究所，UAM-CSIC）；Van Swinderen Institute for Particle Physics and Gravity, University of Groningen（格罗宁根大学范斯温德恩粒子物理与引力研究所）；Departamento de Física Teórica and CIAFF, Universidad Autónoma de Madrid（马德里自治大学理论物理系及CIAFF）
We propose an experimental setup, feasible with present day technology, involving two highquality- factor cavities, one Ramsey zone and a two-level atom which interacts with them. The dynamics in the cavities is modeled by a dissipative dispersive Jaynes-Cummings model. Analytical expresions for the evolution superoperator in each part of the proposed setup and for the concurrence between the atom and the first cavity are given, and the pairwise entanglement of the subsystems is calculated numerically. We consider initial separable states given by the tensor product of a superposition of the t…
We embarked upon the task of experimental protection of different classes of tripartite entangled states, namely the maximally entangled GHZ and W states and the ${\rm W \bar{W}}$ state, using dynamical decoupling. The states were created on a three-qubit NMR quantum information processor and allowed to evolve in the naturally noisy NMR environment. Tripartite entanglement was monitored at each time instant during state evolution, using negativity as an entanglement measure. It was found that the W state is most robust while the GHZ-type states are most fragile against the natural decoherence …
The decoherence in trapped ion induced by coupling the ion to the engineered reservoir is studied in this paper. The engineered reservoir is simulated by random variations in the trap frequency, and the trapped ion is treated as a two-level system driven by a far off-resonant plane wave laser field. The dependence of the decoherence rate on the amplitude of the superposition state is given.
The decoherence of nonclassical motional states of a trapped $^9 {\rm Be^+}$ ion in a recent experiment is investigated theoretically. Sources of decoherence considered here destroy the characteristic coherent quantum dynamics of the system but do not cause energy dissipation. Here they are first introduced phenomenologically and then described using a microscopic Hamiltonian formulation. Theoretical predictions are compared to experimental results.
We present a nonlinear decoherence model which models decoherence effect caused by various decohereing sources in a quantum system through a nonlinear coupling between the system and its environment, and apply it to investigating decoherence in nonclassical motional states of a single trapped ion. We obtain an exactly analytic solution of the model and find very good agreement with experimental results for the population decay rate of a single trapped ion observed in the NIST experiments by Meekhof and coworkers (D. M. Meekhof, {\it et al.}, Phys. Rev. Lett. {\bf 76}, 1796 (1996)).
The control of thermal decoherence via dynamical decoupling and via the quantum Zeno effect (Zeno control) is investigated for a model of trapped ion, where the dynamics of two low lying hyperfine states undergoes decoherence due to the thermal interaction with an excited state. Dynamical decoupling is a procedure that consists in periodically driving the excited state, while the Zeno control consists in frequently measuring it. When the control frequency is high enough, decoherence is shown to be suppressed. Otherwise, both controls may accelerate decoherence.
We consider interactions that generate a universal set of quantum gates on logical qubits encoded in a collective-dephasing-free subspace, and discuss their implementations with trapped ions. This allows for the removal of the by-far largest source of decoherence in current trapped-ion experiments, collective dephasing. In addition, an explicit parametrization of all two-body Hamiltonians able to generate such gates without the system's state ever exiting the protected subspace is provided.
We propose a decoherence-free subspaces (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent Coulomb interaction is exploited, and the universal set of unconventional geometric quantum gates is achieved in encoded subspaces that are immune from decoherence by collective dephasing. The scalability of the scheme for the ion array system is demonstrated, either by an adiabatic way of switching on and off the interactions, or by a fast gate scheme with comprehensive DFS encoding and noise decoupling techniques.
We propose a feasible scheme to achieve holonomic quantum computation in a decoherence-free subspace (DFS) with trapped ions. By the application of appropriate bichromatic laser fields on the designated ions, we are able to construct two noncommutable single-qubit gates and one controlled-phase gate using the holonomic scenario in the encoded DFS.
We study the entanglement between the 2D vibrational motion and two ground state hyperfine levels of a trapped ion, Under particular conditions this entanglement depends on the parity of the total initial vibrational quanta. We study the robustness of this quantum coherence effect with respect to the presence of non-dissipative sources of decoherence, and of an imperfect initial state preparation.
We propose a geometric phase gate in a decoherence-free subspace with trapped ions. The quantum information is encoded in the Zeeman sublevels of the ground-state and two physical qubits to make up one logical qubit with ultra long coherence time. Single- and two-qubit operations together with the transport and splitting of linear ion crystals allow for a robust and decoherence-free scalable quantum processor. For the ease of the phase gate realization we employ one Raman laser field on four ions simultaneously, i.e. no tight focus for addressing. The decoherence-free subspace is left neither …
In this paper, we investigate the dynamics behaviors of genuine multipartite Einstein-Podolsky-Rosen steering (GMS) and genuine multipartite nonlocality (GMN), and explore how to recover the lost GMS and GMN under a mixed decoherence system. Explicitly, the decoherence system can be modeled by that a tripartite Werner-type state suffers from the non-Markovian regimes and one subsystem of the tripartite is under a non-inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner-type state established initially. GMS and GMN are very fragi…
We propose an experimentally feasible scheme for dissipative preparation of tripartite entangled state with atoms separately trapped in an array of three coupled cavities. The combination of coherent driving fields and quantum-jump-based feedback control will drive the system into a non-equilibrium steady state, which has a nearly perfect overlap with the genuine three-atom singlet state. Different control strategies are investigated and the corresponding optimal parameters are confirmed. Moreover, the fidelity of target state is insensitive to detection inefficiencies, and it oversteps 90\% f…
This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localiz…
Analysis of the effects of decoherence on the radiative and squeezing properties of a coherently driven two-level atom trapped in a resonant cavity applying the corresponding master equation is presented. The atomic dynamics as well as the squeezing and statistical properties of the emitted radiation are investigated. It is found that the atom stays in the lower energy level more often at steady state irrespective of the strength of the coherent radiation and thermal fluctuations entering the cavity. Moreover, a strong external coherent radiation results the splitting of the line of the emissi…
Using simple physical arguments we investigate the capabilities of a quantum computer based on cold trapped ions. From the limitations imposed on such a device by spontaneous decay, laser phase coherence, ion heating and other sources of error, we derive a bound between the number of laser interactions and the number of ions that may be used. The largest number which may be factored using a variety of species of ion is determined.
We investigate the mechanism of damping and heating of trapped ions associated with the polarization of the residual background gas induced by the oscillating ions themselves. Reasoning by analogy with the physics of surface electrons in liquid helium, we demonstrate that the decay of Rabi oscillations observed in experiments on 9Be+ can be attributed to the polarization phenomena investigated here. The measured sensitivity of the damping of Rabi oscillations with respect to the vibrational quantum number of a trapped ion is also predicted in our polarization model.
We propose a simple technique for the generation of arbitrary-sized Dicke states in a chain of trapped ions. The method uses global addressing of the entire chain by two pairs of delayed but partially overlapping laser pulses to engineer a collective adiabatic passage along a multi-ion dark state. Our technique, which is a many-particle generalization of stimulated Raman adiabatic passage (STIRAP), is decoherence-free with respect to spontaneous emission and robust against moderate fluctuations in the experimental parameters. Furthermore, because the process is very rapid, the effects of heati…
We analyze collisional decoherence of atoms or molecules prepared in a coherent superposition of nondegenerate internal states at ultralow temperatures and placed in an ultracold buffer gas. Our analysis is applicable for an arbitrary bath particle/tracer particle mass ratio. Both elastic and inelastic collisions contribute to decoherence. We obtain an expression relating the observable decoherence rate to pairwise scattering properties, specifically the low-temperature scattering amplitudes. We consider the dependence on the bath particle/tracer particle mass ratio for the case of light bath …
We measure and characterize anomalous motional decoherence of an atomic ion confined in the lowest quantum levels of a novel rf ion trap that features moveable electrodes. The scaling of decoherence rate with electrode proximity is measured, and when the electrodes are cooled from 300 K to 150 K, the decoherence rate is suppressed by an order of magnitude. This provides direct evidence that anomalous motional decoherence of trapped ions stems from microscopic noisy potentials on the electrodes. These observations are relevant to quantum information processing schemes using trapped ions or othe…
Quantum repeaters provide an efficient solution to distribute Bell pairs over arbitrarily long distances. While scalable architectures are demanding regarding the number of qubits that need to be controlled, here we present a quantum repeater scheme aiming to extend the range of present day quantum communications that could be implemented in the near future with trapped ions in cavities. We focus on an architecture where ion-photon entangled states are created locally and subsequently processed with linear optics to create elementary links of ion-ion entangled states. These links are then used…
We show that trapped ions can be used to simulate a highly symmetrical Hamiltonian with eingenstates naturally protected against local sources of decoherence. This Hamiltonian involves long range coupling between particles and provides a more efficient protection than nearest neighbor models discussed in previous works. Our results open the perspective of experimentally realizing in controlled atomic systems, complex entangled states with decoherence times up to nine orders of magnitude longer than isolated quantum systems.
Maximally entangled states are of utmost importance to quantum communication, dense coding, and quantum teleportation. With a trapped ion placed inside a high finesse optical cavity, interacting with field of an external laser and quantized cavity field, a scheme to generate a maximally entangled three qubit GHZ state, is proposed. The dynamics of tripartite entanglement is investigated, using negativity as an entanglement measure and linear entropy as a measure of mixedness of a state. It is found that (a) the number of modes available to the subsystem determines the maximum entanglement of a…
We investigate the problem of factorization of large numbers on a quantum computer which we imagine to be realized within a linear ion trap. We derive upper bounds on the size of the numbers that can be factorized on such a quantum computer. These upper bounds are independent of the power of the applied laser. We investigate two possible ways to implement qubits, in metastable optical transitions and in Zeeman sublevels of a stable ground state, and show that in both cases the numbers that can be factorized are not large enough to be of practical interest. We also investigate the effect of qua…
We demonstrate long-lived coherence in internal hyperfine states of a single \Ca{43} trapped-ion qubit $[T_2=1.2(2)\s]$, and in external motional states of a single \Ca{40} trapped-ion qubit $[T_2'=0.18(4)\s]$, in the same apparatus. The motional decoherence rate is consistent with the heating rate, which was measured to be 3(1) quanta/sec. Long coherence times in the external motional states are essential for performing high-fidelity quantum logic gates between trapped-ion qubits. The internal-state $T_2$ time that we observe in \Ca{43}, which has not previously been used as a trapped-ion qub…
The dominant error sources for state-of-the-art laser-free trapped-ion entangling gates are decoherence of the qubit state and the ion motion. The effect of these decoherence mechanisms can be suppressed with additional control fields, or with techniques that have the disadvantage of reducing gate speed. Here, we propose using a near-motional-frequency magnetic field gradient to implement a laser-free gate that is simultaneously resilient to both types of decoherence, does not require additional control fields, and has a relatively small cost in gate speed.
Suppressing undesired nonunitary effects is a major challenge in quantum computation and quantum control. In this work, by considering the adiabatic dynamics in presence of a surrounding environment, we theoretically and experimentally analyze the robustness of adiabaticity in open quantum systems. More specifically, by considering a decohering scenario, we exploit the validity conditions of the adiabatic approximation as well as its sensitiveness to the resonance situation, which typically harm adiabaticity in closed systems. As an illustration, we implement an oscillating Landau-Zener Hamilt…
We reckon the behaviour of spin squeezing in tripartite unsqueezed maximally entangled Green- berger-Horne-Zeilinger (GHZ) and W states under various decoherence channels with Kitagawa- Ueda (KU) criteria. In order to search spin squeezing sudden death (SSSD) and signatures of spin squeezing production we use bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels in the present study. In literature, the influence of decoherence has been studied as a destroying element. On the contrary here we investigate the positive aspect of decoherence, which prod…
The Fermi edge singularity and the Anderson orthogonality catastrophe describe the universal physics which occurs when a Fermi sea is locally quenched by the sudden switching of a scattering potential, leading to a brutal disturbance of its ground state. We demonstrate that the effect can be seen in the controllable domain of ultracold trapped gases by providing an analytic description of the out-of-equilibrium response to an atomic impurity, both at zero and at finite temperature. Furthermore, we link the transient behavior of the gas to the decoherence of the impurity, and, in particular to …
Physical systems must fulfill a number of conditions to qualify as useful quantum bits (qubits) for quantum information processing, including ease of manipulation, long decoherence times, and high fidelity readout operations. Since these conditions are hard to satisfy with a single system, it may be necessary to combine different degrees of freedom. Here we discuss a possible system, based on electronic and nuclear spin degrees of freedom in trapped ions. The nuclear spin yields long decoherence times, while the electronic spin, in a magnetic field gradient, provides efficient manipulation, an…
We study theoretically the possibilities of coupling the quantum mechanical motion of a trapped charged particle (e.g. ion or electron) to quantum degrees of freedom of superconducting devices, nano-mechanical resonators and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e. the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examin…
We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of $10^{-3}$ for each operation. Current limitations and possible approaches to further improvement of the device are discussed.
We present a scheme utilizing position-dependent ac Stark shifts for doing quantum logic with trapped ions. By a proper choice of direction, position and size, as well as power and frequency of a far-off-resonant Gaussian laser beam, specific ac Stark shifts can be assigned to the individual ions, making them distinguishable in frequency-space. In contrast to previous all-optical based quantum gates with trapped ions, the present scheme enables individual addressing of single ions and selective addressing of any pair of ions for two-ion quantum gates, without using tightly focused laser beams.…
A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling'', is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the Sorensen-Molmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme d…
We present a quantum interference approach to preserve coherence in the external states of an atom trapped in an optical lattice. We show that this is possible by suitably choosing the initial state of the atom. We demonstrate this in context of decoherence due to spontaneous emission in an one-dimensional optical double-well lattice.
Quantum computing gates are proposed to apply on trapped ions in decoherence-free states. As phase changes due to time evolution of components with different eigenenergies of quantum superposition are completely frozen, quantum computing based on this model would be perfect. Possible application of our scheme in future ion-trap quantum computer is discussed.
We investigate the capabilities of a quantum computer based on cold trapped ions in presence of non-dissipative decoherence. The latter is accounted by using the evolution time as a random variable and then averaging on a properly defined probability distribution. Severe bounds on computational performances are found.
The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization. It can be reconstructed from an ensemble of copies, by performing measurements on different realizations. Reconstructing the state of a set of trapped particles shielded from their environment is an important step for the investigation of the quantum to classical boundary. While trapped atom state reconstructions have been achieved, it is challenging to perfo…
We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum, non-relativistic particles. We solve the Schrödinger equation for the wave function of this tripartite system using exact diagonalization. Although computational limitations on the size of the Hilbert space prevent us from exploring the regime where the device and environment consist of a truly macroscopic number of degrees of freedom, we nevertheless see clear …
We use a spin-1/2 model to analyze tunnelling in a double well system coupled to an external reservoir. We consider different noise sources such as fluctuations on the height and central position of the barrier and propose an experiment to observe these effects in trapped ions or atoms.
