Efficient vibrational state coupling in an optical tilted-washboard potential via multiple spatial translations and application to pulse echoes

Abstract

We measure the application of simple and compound pulses consisting of time-dependent spatial translations to coupling vibrational states of ultracold 85 Rb atoms in a far-detuned 1D optical lattice. The lattice wells are so shallow as to support only two bound states, and we prepare the atoms in the ground state. The lattice is oriented vertically, leading to a tilted-washboard potential analogous to those encountered in condensed-matter systems. Experimentally, we find that a square pulse consisting of lattice displacements and a delay is more efficient than single-step and Gaussian pulses. This is described as an example of coherent control. It is striking that contrary to the intuition that soft pulses minimize loss, the Gaussian pulse is outperformed by the square pulse. Numerical calculations are in strong agreement with our experimental results and show the superiority of the square pulse to the single-step pulse for all lattice depths and to the Gaussian pulse for lattice depths greater than 7 lattice recoil energies. We also compare the effectiveness of these pulses for reviving oscillations of atoms in vibrational superposition states using the pulse-echo technique. We find that the square and Gaussian pulses result in higher echo amplitudes than the single-step pulse. These improved echo pulses allow us to probe coherence at longer times than in the past, measuring a plateau which has yet to be explained. In addition, we show numerically that the vibrational state coupling due to such lattice manipulations is more efficient in shallow lattices than in deep lattices. The coupling probability for an optimized single-step pulse approaches 1/e as the depth goes to infinity (harmonic-oscillator limit), while in shallow lattices with large anharmonicity, the coupling probability reaches a maximum value of 0.51 for a lattice depth of 5 recoil energies. For square and Gaussian pulses the coupling in the lattice is even stronger, reaching maxima of 0.64 at 6 recoil energies and 0.67 at 5 recoil energies, respectively.

Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator

“…For the lowest few levels, superconducting qubits of the transmon [15], phase qubit [19], and capacitively shunted flux qubit [16] types are well approximated by a SNO. Furthermore, motional states in optical lattices [24], collective modes of ion traps [26] and nanomechanical oscillators [34] are also described as SNOs.…”

“…In fact, it has been shown that no physical particle can be a true qubit [23]. Examples of leakage states include higher vibrational states in optical lattices [24], polarized spin states in the singlet-triplet qubits [25], and auxiliary states in ion traps [26] and Rydberg atoms [27][28][29].…”

High-fidelity quantum gates in the presence of dispersion

“…Here E R = 2 k 2 L /2m is the recoil energy, i.e., the kinetic energy the atom gains by absorbing a lattice photon. At these lattice depths for typical atomic densities the atoms are essentially non-interacting [11] and thus we can simplify the model by considering the evolution of a single atom.…”

“…We consider a physical model of the optical lattice similar to the experimental apparatus described in Refs [11,31,32]. The optical lattice potential is generated by two vertical counter-propagating lasers with an incidence angle of 49.6 • and is loaded with 85 Rb atoms from an optical molasses at 10 µK.…”

“…This generates a trapping potential in which sufficiently cold atoms can be bound and trapped in a one-dimensional periodic potential but can move freely in the other two spatial dimensions. It also provides an opportunity to investigate a difficult control problem in state evolution, particularly from the perspective of quantum computation with qubits formed by the vibrational states of atoms in the lattice, so-called external qubits [9][10][11][12].…”