Robust quantum logic in neutral atoms via adiabatic Rydberg dressing

Editors' Suggestion

Robust quantum logic in neutral atoms via adiabatic Rydberg dressing

Tyler Keating, Robert L. Cook, Aaron M. Hankin, Yuan-Yu Jau, Grant W. Biedermann, and Ivan H. Deutsch

Phys. Rev. A 91, 012337 – Published 28 January 2015

Abstract

We study a scheme for implementing a controlled-Z (cz) gate between two neutral-atom qubits based on the Rydberg blockade mechanism in a manner that is robust to errors caused by atomic motion. By employing adiabatic dressing of the ground electronic state, we can protect the gate from decoherence due to random phase errors that typically arise because of atomic thermal motion. In addition, the adiabatic protocol allows for a Doppler-free configuration that involves counterpropagating lasers in a $σ_{+} / σ_{-}$ orthogonal polarization geometry that further reduces motional errors due to Doppler shifts. The residual motional error is dominated by dipole-dipole forces acting on doubly excited Rydberg atoms when the blockade is imperfect. For reasonable parameters, with qubits encoded into the clock states of ${}^{133}{Cs}$ , we predict that our protocol could produce a cz gate in $< 10$ $μ s$ with error probability on the order of $10^{- 3}$ .

Received 24 November 2014

DOI:https://doi.org/10.1103/PhysRevA.91.012337

Authors & Affiliations

Tyler Keating^1,2, Robert L. Cook^1,2, Aaron M. Hankin^1,2,3, Yuan-Yu Jau^1,3, Grant W. Biedermann^1,2,3, and Ivan H. Deutsch^1,2

¹Center for Quantum Information and Control (CQuIC), University of New Mexico, Albuquerque, New Mexico 87131, USA
²Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
³Sandia National Laboratories, Albuquerque, New Mexico 87185, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 91, Iss. 1 — January 2015

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Schematic for the cphase gate. Two cesium atoms are trapped and cooled in dipole traps, several $μ m$ apart. During the cphase gate, the trapping lasers are turned off and the atoms are illuminated by a 319-nm Rydberg laser. A bias magnetic field ensures that the laser's propagation axis coincides with the atomic quantization axis. (b) In each atom, the logical- $| 0 〉$ state is coupled to a $| 84 P_{3 / 2}; M_{J} 〉$ Rydberg state. The coupling laser has Rabi rate $Ω$ and detuning from atomic resonance $Δ_{0}$ , with a momentum-dependent Doppler shift $δ_{D} \equiv k_{l} p / m$ . (c) In the two-atom basis, $| 00 〉$ is coupled to the bright state $| B 〉$ , again with base detuning $Δ_{0}$ and Doppler shift $δ_{D}$ . Excitation to $| r r 〉$ is blockaded by the dipole-dipole interaction $V_{d d}$ . Atomic motion further couples $| B 〉$ to a dark state $| D 〉$ , outside the ideal blockade subspace.
Reuse & Permissions
Figure 2
Pulse shape and bare state populations over the course of a gate with experimentally feasible parameters: pulse rise time 1 $μ s$ , Rabi frequency sweep $Ω / 2 π = 0 \to$ 3 MHz, detuning sweep $Δ / 2 π = 6 \to$ 0 MHz, Rydberg decay rate $Γ / 2 π$ = 3.7 kHz (blackbody limited lifetime), and interatomic separation $r = 5$ $μ m$ . As the laser turns on and is tuned to resonance, the bare ground state (red) is dressed by admixing significant bright state (blue) population, while the blockaded $| r r 〉$ state (green) remains mostly unpopulated. Adiabaticity and available interaction strength set comparable constraints in this case, so that the laser pulse shape that best achieves the desired evolution is neither square-topped nor triangular.
Reuse & Permissions
Figure 3
(a) Schematic for the “Doppler-free” configuration. Two cesium atoms are trapped and cooled in dipole traps, several $μ m$ apart. During the cphase gate, the trapping lasers are turned off and the atoms are illuminated by two counterpropagating, 319-nm Rydberg lasers. The two Rydberg lasers have opposite circular polarizations, so they couple the atoms to orthogonal magnetic sublevels of the Rydberg manifold. Both Rydberg lasers propagate along the interatomic separation axis; a bias magnetic field ensures that this coincides with the atomic quantization axis. (b) In each atom, counterpropagating lasers couple the logical- $| 0 〉$ state to the $m_{J} = \pm \frac{3}{2}$ magnetic sublevels of the $| 84 P_{3 / 2} 〉$ Rydberg manifold. The two lasers have the same Rabi rate $Ω / \sqrt{2}$ and detuning from resonance $Δ_{0}$ , but experience opposite Doppler shifts, $δ_{D} \equiv k_{L} p / m$ . Zeeman splitting should be made large enough that coupling to $m_{J} = \pm \frac{1}{2}$ can be neglected. (c) In the two-atom basis, the states $| 00 〉$ , $| B_{+} 〉$ , and $| r_{+} r_{+} 〉$ are coupled by the ideal blockade Hamiltonian with no Doppler shifts. Instead, motional noise manifests as a coupling to the dark states $| D_{-} 〉$ and $| B_{-} 〉$ . Because $| D_{-} 〉$ and $| B_{-} 〉$ are outside the ideal adiabatic basis, we can suppress the effects of this coupling through adiabatic evolution.
Reuse & Permissions
Figure 4
Simulated gate error rates ( $1 - F$ ) as a function of adiabatic ramp time. The upper pair of curves was generated with the parameters given in Fig. 2, while the lower curves used a higher Rabi rate for the exciting laser. Ignoring interatomic forces but including all other errors (green triangles), the higher Rabi rate improves both gate speed and fidelity. Including interatomic forces (red circles), any gain in fidelity from the increased speed is offset by stronger forces owing to a larger $| r r 〉$ population when the blockade is imperfect. This suggests that beyond a certain threshold, increased laser power requires a commensurately stronger blockade interaction in order to improve fidelity.
Reuse & Permissions
Figure 5
Simulated gate error rates ( $1 - F$ ) as a function of adiabatic ramp time. For comparison, the red triangle curve ignores motional effects and includes errors due solely to diabatic transitions and finite Rydberg lifetime. For ramp times significantly below 1 $μ s$ , all curves predict low fidelities because the gate is not adiabatic. As the ramp time and adiabaticity are increased, other error sources become limiting factors. Including all error sources while using the Doppler-free configuration (blue circles), we can reach error rates of $\sim 2 \times 10^{- 3}$ , with finite blockade strength as the primary fidelity-limiting factor. By contrast, the single-laser configuration (green squares) suffers more than an order of magnitude greater error than its counterparts.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information