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arXiv:1504.05341 · Journal of Physics B Atomic Molecular and Optical Physics

Optimization of phonon dynamics protocols in ion traps

Tarun Dutta, M Mukherjee, K Sengupta

Published Feb 15, 2016• 2 citations
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Abstract

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.

DOI
10.1088/0953-4075/49/5/055502

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•Jan 1, 2015•0 citations
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 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.
Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.
In this article we present a comprehensive theoretical investigation of phonon lasing with mixed-species trapped ions, as demonstrated in [T. Behrle, Phys. Rev. Lett. 131 (2023)], employing both a semi-classical mean-field description and a full quantum theory. We derive an analytic expression for the second-order coherence function, confirming the experimental observation of the system's lasing behaviour above threshold. Building on the successful implementation of the two-ion lasing scheme, we propose a novel approach for achieving phonon lasing with a single trapped ion, offering significant experimental advantages and making the implementation of multiple phonon lasers within a single setup feasible. Furthermore, we explore lasing in a squeezed basis and in different regimes of the Lamb-Dicke approximation, highlighting the potential to produce non-classical states with promising applications in precision sensing. Our analysis of a sensing protocol based on squeezed states, using experimentally feasible parameters, shows a sensitivity enhancement of up to two orders of magnitude.
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.
This thesis describes schemes for both a fast two-qubit gate operation and the steady-state preparation of a Bell state with trapped ions. A critical figure of merit for quantum computing with trapped ions is the gate duration relative to the decoherence timescale. We propose a fast gate scheme that off ers improvements in time, fidelity and simplicity of implementation over existing fast gate proposals. Our scheme can operate on both neighbouring and non-neighbouring ions in a long ion crystal. This provides a simpler and faster mechanism than traditional gates for complex quantum computing operations on large numbers of ions. The scheme achieves fidelities well above quantum error correction thresholds around 0.0001, and operates arbitrarily fast given arbitrary laser repetition rates. The production of these ultra-fast pulses is an experimental challenge, and fast gates have not yet been implemented; we present an implementation scheme using pulse splitting to provide a higher repetition rate and the pulse timing freedoms required for the gate scheme. We also analyse the effects of errors in the pulses on the gate operation. We analyse another strategy to generate entanglement using a driven dissipative process. Typically, environmental couplings cause decoherence. However, by combining dissipative dynamics with suitably chosen Hamiltonian evolution, the system can be steered to the desired steady states. Our steady-state scheme prepares a maximally-entangled Bell state with fidelity above 0.99, much higher than for schemes implemented with trapped ions. The driven dissipation continuously pumps the system towards the antisymmetric Bell steady-state, which is dark to the system dynamics and robust to parameter variations. The dominant loss mechanism is anomalous heating of the motional modes, reducing our fidelity by less than 0.01 for current experimental rates. Our scheme jointly addresses the ions and does not use sympathetic cooling. We enhance our scheme by combining the dissipative state preparation with the detection of photons, and obtain a significant fidelity enhancement.