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Quantum Information and Computation

Analytical evidence of ultrafast generation of spin-motion entanglement

Kuo Hai, Yunrong Luo, Guishu Chong, Hao Chen, Wenhua Hai

Published Apr 1, 2017• 10 citations
Publisher

Abstract

We investigate ultrafast generation of spin-motion entanglement of a trapped and Gaussian-pulse-kicked two-level ion in the Lamb-Dicke limit and high field regime. A set of exact motional states and the probabilities occupying different pseudospin states are derived and the visible differences between the results with those of the delta-kick case are shown during a kick moment, which analytically evidence the ultrafast generation of an exact spin-motion entangled state regardless of initial state. Our results can be justified with the current experimental capability and provide an analytical method for further study of the ultrafast entanglement in atomic qubits.

DOI
10.26421/qic17.5-6-5

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We investigate ultrafast generation of spin-motion entanglement of a trapped and Gaussian-pulse-kicked two-level ion in the Lamb-Dicke limit and high field regime. A set of exact motional states and the probabilities occupying different pseudospin states are derived and the visible differences between the results with those of the delta-kick case are shown during a kick moment, which analytically evidence the ultrafast generation of an exact spin-motion entangled state regardless of initial state. Our results can be justified with the current experimental capability and provide an analytical method for further study of the ultrafast entanglement in atomic qubits.
We investigate quantum dynamics of a two-level ion trapped in the Lamb-Dicke regime of a δ-kicked optical lattice, based on the exact generalized coherent states rotated by a π/2 pulse of Ramsey type experiment. The spatiotemporal evolutions of the spin-motion entangled states in different parameter regions are illustrated, and the parameter regions of different degrees of quantum stability described by the quantum fidelity are found. Time evolutions of the probability for the ion being in different pseudospin states reveal that the ultrafast entanglement generation and population transfers of the system can be analytically controlled by managing the laser pulses. The probability in an initially disentangled state shows periodic collapses (entanglement) and revivals (de-entanglement). Reduction of the stability degree results in enlarging the period of de-entanglement, while the instability and potential chaos will cause the sustained entanglement. The results could be justified experimentally in the existing setups and may be useful in engineering quantum dynamics for quantum information processing.
We demonstrate quantum entanglement of two trapped atomic ion qubits using a sequence of ultrafast laser pulses. Unlike previous demonstrations of entanglement mediated by the Coulomb interaction, this scheme does not require confinement to the Lamb-Dicke regime and can be less sensitive to ambient noise due to its speed. To elucidate the physics of an ultrafast phase gate, we generate a high entanglement rate using just ten pulses, each of ∼20 ps duration, and demonstrate an entangled Bell state with (76±1)% fidelity. These results pave the way for entanglement operations within a large collection of qubits by exciting only local modes of motion.
Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of entangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This approach can limit the speed of entangling gates and make them vulnerable to decoherence due to coupling to unwanted modes or ion heating. This thesis is directed towards demonstrating novel entanglement schemes which are not limited by the trap frequency, and can be made almost arbitrarily fast. Towards this goal, I report here on the first experiments using ultrafast laser pulses to control the internal and external states of a single trapped ion. I begin with experiments in ultrafast spin control, showing how a single laser pulse can be used to completely control both spin degrees of freedom of the ion qubit in tens of picoseconds. I also show how a train of weak pulses can be used to drive Raman transitions based on a frequency comb. I then discuss experiments using pulses to rapidly entangle the spin with the motion, and how careful spectral redistribution allows a single pulse to execute a spin-dependent momentum kick. Finally, I explain how these spin-dependent momentum kicks can be used in the future to create an ultrafast entangling gate. I go over how such a gate would work, and present experimentally realizable timing sequences which would create a maximally entangled state of two ions in a time faster than the period of motion in the trap.
Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of en-tangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This approach can limit the speed of entangling gates and make them vulnerable to decoherence due to coupling to unwanted modes or ion heating. This thesis is directed towards demon-strating novel entanglement schemes which are not limited by the trap frequency, and can be made almost arbitrarily fast. Towards this goal, I report here on the first experiments using ultrafast laser pulses to control the internal and external states of a single trapped ion. I begin with experiments in ultrafast spin control, showing how a single laser pulse can be used to completely control both spin degrees of freedom of the ion qubit in tens of picoseconds. I also show how a train of weak pulses can be used to drive Raman transitions based on a frequency comb. I then discuss exper-iments using pulses to rapidly entangle the spin with the motion, and how careful spectral redistribution allows a single pulse to execute a spin-dependent momentum kick. Finally, I explain how these spin-dependent momentum kicks can be used in the future to create an ultrafast entangling gate. I go over how such a gate would work, and present experimentally realizable timing sequences which would create a maximally entangled state of two ions in a time faster than the period of motion in the trap.
We report entanglement of a single atom's hyperfine spin state with its motional state in a time scale of less than 3 ns. We engineer a short train of intense laser pulses to impart a spin-dependent momentum transfer of ± 2 ħk. Using pairs of momentum kicks, we create an atomic interferometer and demonstrate collapse and revival of spin coherence as the motional wave packet is split and recombined. The revival after a pair of kicks occurs only when the second kick is delayed by an integer multiple of the harmonic trap period, a signature of entanglement and disentanglement of the spin with the motion. Such quantum control opens a new regime of ultrafast entanglement in atomic qubits.
Ultrafast spin-phonon entanglement based on spin-dependent momentum kicks (SDKs) provides an approach to realize fast entangling gates with intrinsic robustness and scalability for trapped ion quantum computing. Such SDKs so far have been implemented on a nanosecond timescale by off-resonant Raman transitions where each laser pulse is split into a sequence of perturbation pulses with carefully designed temporal patterns. Here we report an experimental realization of ultrafast qubit manipulation and spin-phonon entanglement in picoseconds using SDKs from single resonant laser pulses on the magnetic-field-insensitive hyperfine qubit states. This experiment demonstrates a convenient approach to ultrafast SDKs on noise-insensitive ion-spin qubits, with improvement in its speed by more than an order of magnitude. It removes the need to engineer the pattern of a sequence of perturbation pulses and is less vulnerable to noise, simplifying the approach to large-scale trapped-ion quantum computing based on fast quantum gates with SDKs.