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arXiv:1305.5555 · Physical Review Letters

Ramp Dynamics of Phonons in an Ion Trap: Entanglement Generation and Cooling

Tarun Dutta, Manas Mukherjee, K. Sengupta

Published Oct 25, 2013• 7 citations
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Abstract

We show that the ramp dynamics of phonons in a one-dimensional ion trap can be used for both generating multiparticle entangled states and motional state cooling of a string of trapped ions. We study such ramp dynamics using an effective Bose-Hubbard model which describes these phonons at low energies and show that specific protocols, involving site-specific dynamical tuning of the on-site potential of the model, can be used to generate entangled states and to achieve motional state cooling without involving electronic states of the ions. We compare and contrast our schemes for these to the earlier suggested ones and discuss specific experiments to realize the suggested protocols.

DOI
10.1103/physrevlett.111.170406

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We show that the ramp dynamics of phonons in a one-dimensional ion trap can be used for both generating multiparticle entangled states and motional state cooling of a string of trapped ions. We study such ramp dynamics using an effective Bose-Hubbard model which describes these phonons at low energies and show that specific protocols, involving site-specific dynamical tuning of the on-site potential of the model, can be used to generate entangled states and to achieve motional state cooling without involving electronic states of the ions. We compare and contrast our schemes for these to the earlier suggested ones and discuss specific experiments to realize the suggested protocols.
Abstract We develop a theory to address the non equilibrium dynamics of phonons in a one-dimensional finite size trapped ion system for non linear ramp and periodic protocols. Our analysis, which is based on our earlier proposal of dynamics-induced cooling and entanglement generation between phonons in these systems when subjected to a linear ramp protocol [1], identifies the optimal protocol within the above-mentioned classes, which minimizes both the cooling and entanglement generation time. We also introduce single-/two-site addressing to achieve cooling/entanglement, which is expected to lead to simpler implementation of these protocols. Finally, we discuss the effect of noise due to the fluctuation of the intensity of the laser used to generate the trap on entanglement generation. We also discuss realistic experimental setups that may serve as test beds for our theory.
We propose a concrete experiment to probe the nonequilibrium local dynamics of the one-dimensional Bose-Hubbard model using a trapped ion system consisting of a linear chain of few ions prepared in a state of transverse motional mode which corresponds to a fixed number of phonons per ion. These phonons are well known to be described by an effective Bose-Hubbard model. We propose a protocol which leads to a sudden local sign reversal of the on-site interaction strength of this Hubbard model at one of the sites and demonstrate that the subsequent nonequilibrium dynamics of the model can be experimentally probed by measuring the time-dependent phonon number in a specific motional state of the ions. We back our experimental proposal with exact numerical calculation of the dynamics of a Bose-Hubbard model subsequent to a local quench.
We propose an efficient method to produce multiparticle entangled states of ions in an ion trap for which a wide range of interesting effects and applications have been suggested. Our preparation scheme exploits the collective vibrational motion of the ions, but it works in such a way that this motion need not be fully controlled in the experiment. The ions may, e.g., be in thermal motion and exchange mechanical energy with a surrounding heat bath without detrimental effects on the internal state preparation. Our scheme does not require access to the individual ions in the trap.
This thesis is devoted to the theoretical study of strongly correlated quantum many-body states with trapped ions interacting with lasers. A system of trapped ions under the action of off--resonant standing--waves can be used to simulate a variety of quantum interacting models. Based on this idea we study in detail effective quantum spin models and Bose-Hubbard model in ion traps. Our numerical calculations with the DMRG show that experiments with ion traps should allow one to access general properties of quantum critical systems. Ion trap quantum spin models and Bose-Hubbard model show novel features due to the peculiarities of induced effective spin-spin and phonon-phonon interactions.
We consider a degenerate Bose gas confined in a double-well potential in interaction with a trapped ion in one dimension and investigate the impact of two relevant sources of imperfections in experiments on the system dynamics: ion motion and thermal excitations of the bosonic ensemble. Particularly, their influence on the entanglement generation between the spin state of the moving ion and the atomic ensemble is analyzed. We find that the detrimental effects of the ion motion on the entanglement protocol can be mitigated by properly choosing the double-well parameters as well as timings of the protocol. Furthermore, thermal excitations of the bosons affect significantly the system's tunneling and self-trapping dynamics at moderate temperatures; i.e., thermal occupation of a few double-well quanta reduces the protocol performance by about 10%. Hence, we conclude that finite temperature is the main source of decoherence in such junctions and we demonstrate the possibility to entangle the condensate motion with the ion vibrational state.
A scheme is proposed to generate an arbitrary entangled state of the two-dimensional vibrational motion of a trapped ion. In the scheme the ion is excited by a sequence of laser pulses tuned to the appropriate vibrational sidebands. In order to generate a pure state with upper phonon numbers M and N in the X and Y directions, respectively, we require no more than (M+2)(N+1)(M+2)(N+1)(M+2)(N+1) operations.