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arXiv:2204.04007 · Physical Review A

Optical control of the complex phase of a quantum ground-state amplitude

Adam Kinos, Mogens Dalgaard, Klaus Mølmer

Published Jun 23, 2022• 3 citations
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Abstract

We discuss how coherent driving of a two-level quantum system can be used to induce a complex phase on the ground state and we discuss its geometric and dynamic contributions. While the global phase of a wave function has no physical significance, the coherent dynamics in a two-level subspace provides relative phases and is an essential building block for more advanced dynamics in larger systems. In this regard, we note that one must be careful with intuitive accounts of the phase dynamics as it depends on the interaction picture applied. To mitigate ambiguities in practical analyses, we suggest to complement the Bloch sphere picture with the path taken by the ground-state amplitude in the complex plane, and we show how the two-level pure-state dynamics can serve as a starting point for the study of the dynamics explored in three-level lambda systems, four-level tripod systems, and open quantum systems.

DOI
10.1103/physreva.105.062441

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We discuss how coherent driving of a two-level quantum system can be used to induce a complex phase on the ground state and we discuss its geometric and dynamic contributions. While the global phase of a wave function has no physical significance, the coherent dynamics in a two-level subspace provides relative phases and is an essential building block for more advanced dynamics in larger systems. In this regard, we note that one must be careful with intuitive accounts of the phase dynamics as it depends on the interaction picture applied. To mitigate ambiguities in practical analyses, we suggest to complement the Bloch sphere picture with the path taken by the ground-state amplitude in the complex plane, and we show how the two-level pure-state dynamics can serve as a starting point for the study of the dynamics explored in three-level lambda systems, four-level tripod systems, and open quantum systems.
Practical and robust control of the complex phases of qubit superposition states is necessary for high-fidelity quantum gates. Here we experimentally demonstrate such control in a trapped ultracold 40 Ca + ion, where the phase of qubit ground state is modified by optical driving to an excited state. Using a third spectator quantum level as reference, we experimentally measure the phases generated on the ground state amplitude by different driving schemes. While geometric phases exhibit intrinsic robustness to systematic control errors due to their dependence on global geometric properties (e.g., Berry curvature) rather than dynamical details, their resilience to decoherence remains a topic requiring critical clarification. In this work, we show that geometric phases are not in general immune to environment-induced decoherence, and their practical robustness, including to decoherence, depends on active error-suppression strategies. We implement different driving schemes and find that minimizing excited state decay is more decisive for their robustness on decoherence than whether the phase is of a geometric or dynamical character. This work established and demonstrated a new control strategy that mitigates decoherence effects in geometric/complex phase systems, compensating for their susceptibility to decoherence. We experimentally benchmark four phase-imprinting protocols under a tunable engineered dissipation channel and controlled systematic errors in a single trapped-ion qubit. Our central quantitative finding is that the sensitivity to decoherence is governed by the time-integrated excited-state population, rather than by whether the accumulated phase is labeled geometric or dynamical.
The manipulation of the steady-state behavior of a collection of dipole-interacting three-level atoms in a V or Lambda configuration is investigated as a function of the relative phase of two strong coherent driving fields. For larger samples, the phase is shown to be a convenient parameter to rapidly populate or depopulate completely a trapping state of the ensemble. As applications, we present the appropriately prepared atomic sample as an optical switching device and show its virtues in controlling the collective steady-state resonance fluorescence intensity.
We use a combination of microwave fields and free precession to drive the spin of a nitrogen-vacancy (NV) center in diamond on different trajectories on the Bloch sphere and investigate the physical significance of the frame-dependent decomposition of the total phase into geometric and dynamic parts. The experiments are performed on a two-level subspace of the spin-1 ground state of the NV, where the Aharonov-Anandan geometric phase manifests itself as a global phase, and we use the third level of the NV ground-state triplet to detect it. We show that while the geometric Aharonov-Anandan phase retains its connection to the solid angle swept out by the evolving spin, it is generally accompanied by a dynamic phase that suppresses the geometric dependence of the system dynamics. These results offer insights into the physical significance of frame-dependent geometric phases.
We examine the absorption of a weak probe beam in a laser-driven tripod-type atom with three closely lying ground levels, where both the driving and probe lasers interact simultaneously with the three transitions. The effects of spontaneously generated coherence (SGC) are taken into account. We introduce dipole moments in the dressed-state picture and the Hamiltonian in terms of the dressed states describing the interaction between the probe and the atom. Gain spectrum under various conditions are presented and analyzed. We show that the spectral structure and the gain amplitude of the probe are strongly influenced by the effect of SGC and the frequency separation of the three closely lying ground levels. The tripod-type atomic system with quantum interference in spontaneous emission can be simulated in the dressed-state picture of a coherently driven four-level N-type system where no SGC effect exists.