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Iranian Journal of Physics Research

Quantum speed limit in producing atom-ion entanglement in Josephson junction

Shahpoor Saeidian, Mostafa R. Ebgha

Published Oct 1, 2020• 0 citations
Publisher

Abstract

In this work, we have studied the tunneling of a single atom in a double-well. The atom is interacting with a single ion in a simple harmonic trap placed in the center of the double-well. The tunneling of the atom is controlled by the spin and/or motional state of the ion. Considering a model potential, we have shown that it is possible to generate an entangled state between the spatial state of the ion and the atomic wavefunction. By employing the optimal control method, the quantum speed limit of generating this entangled process has been explored. This system can be used as qubit in quantum computers.

DOI
10.47176/ijpr.20.3.38821

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In this work, we have studied the tunneling of a single atom in a double-well. The atom is interacting with a single ion in a simple harmonic trap placed in the center of the double-well. The tunneling of the atom is controlled by the spin and/or motional state of the ion. Considering a model potential, we have shown that it is possible to generate an entangled state between the spatial state of the ion and the atomic wavefunction. By employing the optimal control method, the quantum speed limit of generating this entangled process has been explored. This system can be used as qubit in quantum computers.
We theoretically investigate the properties of a double-well bosonic Josephson junction coupled to a single trapped ion. We find that the coupling between the wells can be controlled by the internal state of the ion, which can be used for studying mesoscopic entanglement between the two systems and to measure their interaction with high precision. As a particular example we consider a single ^{87}Rb atom and a small Bose-Einstein condensate controlled by a single 171Yb+ ion. We calculate interwell coupling rates reaching hundreds of Hz, while the state dependence amounts to tens of Hz for plausible values of the currently unknown s-wave scattering length between the atom and the ion. The analysis shows that it is possible to induce either the self-trapping or the tunneling regime, depending on the internal state of the ion. This enables the generation of large scale ion-atomic wave packet entanglement within current technology.
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.
We analyze theoretically the dynamics of an atomic double-well system with a single ion trapped in its center. We find that the atomic tunneling rate between the wells depends both on the spin of the ion via the short-range spin-dependent atom-ion scattering length and on its motional state with tunneling rates reaching hundreds of hertz. A protocol is presented that could transport an atom from one well to the other, depending on the motional (Fock) state of the ion within a few milliseconds. This phonon-atom coupling is of interest for creating atom-ion entangled states and may form a building block in constructing a hybrid atom-ion quantum simulator. We also analyze the effect of imperfect ground-state cooling of the ion and the role of micromotion when the ion is trapped in a Paul trap. Due to the strong nonlinearities in the atom-ion interaction, the micromotion can cause couplings to high-energy atom-ion scattering states, preventing accurate state preparation and complicating the double-well dynamics. We conclude that the effects of micromotion can be reduced by choosing ion-atom combinations with a large mass ratio and by choosing large interwell distances. The proposed double-well system may be realized in an experiment by combining either optical traps or magnetic microtraps for atoms with ion trapping technology.
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.
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.
By means of optimal control techniques we model and optimize the manipulation of the external quantum state (center-of-mass motion) of atoms trapped in adjustable optical potentials. We consider in detail the cases of both noninteracting and interacting atoms moving between neighboring sites in a lattice of a double-well optical potentials. Such a lattice can perform interaction-mediated entanglement of atom pairs and can realize two-qubit quantum gates. The optimized control sequences for the optical potential allow transport faster and with significantly larger fidelity than is possible with processes based on adiabatic transport.