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Physical Review A

In-phase and antiphase dynamics of Rydberg atoms with distinguishable resonances

Chu-Hui Fan, Han-Xiao Zhang, Jin-Hui Wu

Published Mar 6, 2019• 7 citations
Publisher

Abstract

We study the correlated evolutions of two Rydberg atoms, interacting via a van der Waals (vdW) potential ${V}_{6}$ and driven by a laser field of detunings ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$. The two atoms may exhibit the in-phase dynamics with identical Rydberg populations or the antiphase dynamics with complementary Rydberg populations, depending on their initial states. For a moderate vdW potential far from the blockade regime, the in-phase or antiphase dynamics can be attained along two intersecting lines in the parameter space of ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ with an exact or approximate figure of merit, respectively. Note, in particular, that the exact in-phase dynamics is trivial because it requires identical detunings while the approximate in-phase, exact antiphase, and approximate antiphase dynamics are nontrivial because they require distinct detunings. The specific requirements on ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ for both in-phase and antiphase dynamics can be understood by considering the balanced transitions from two initially populated states to two initially empty states in the double-atom state basis.

DOI
10.1103/physreva.99.033813

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We study the correlated evolutions of two Rydberg atoms, interacting via a van der Waals (vdW) potential V6{V}_{6}V6​ and driven by a laser field of detunings \ensuremathΔ1{\mathrm{\ensuremath{\Delta}}}_{1}\ensuremathΔ1​ and \ensuremathΔ2{\mathrm{\ensuremath{\Delta}}}_{2}\ensuremathΔ2​. The two atoms may exhibit the in-phase dynamics with identical Rydberg populations or the antiphase dynamics with complementary Rydberg populations, depending on their initial states. For a moderate vdW potential far from the blockade regime, the in-phase or antiphase dynamics can be attained along two intersecting lines in the parameter space of \ensuremathΔ1{\mathrm{\ensuremath{\Delta}}}_{1}\ensuremathΔ1​ and \ensuremathΔ2{\mathrm{\ensuremath{\Delta}}}_{2}\ensuremathΔ2​ with an exact or approximate figure of merit, respectively. Note, in particular, that the exact in-phase dynamics is trivial because it requires identical detunings while the approximate in-phase, exact antiphase, and approximate antiphase dynamics are nontrivial because they require distinct detunings. The specific requirements on \ensuremathΔ1{\mathrm{\ensuremath{\Delta}}}_{1}\ensuremathΔ1​ and \ensuremathΔ2{\mathrm{\ensuremath{\Delta}}}_{2}\ensuremathΔ2​ for both in-phase and antiphase dynamics can be understood by considering the balanced transitions from two initially populated states to two initially empty states in the double-atom state basis.
We study the correlated evolutions of two far-spaced Rydberg atomic pairs with different resonant frequencies, interacting via van der Waals (vdW) potentials and driven by a common laser field. They are found to exhibit in-phase (anti-phase) beating dynamics characterized by identical (complementary) intra-pair entanglements under a specific condition in regard of inter-pair vdW potentials and driving field detunings. This occurs when each atomic pair just oscillates between its ground state and symmetric entangled state because its doubly excited state and asymmetric entangled state are forbidden due to rigid dipole blockade and perfect destructive interference, respectively. More importantly, optimal inter-pair overall entanglement can be attained at each beating node corresponding to semi-optimal intra-pair entanglements, and inevitable dissipation processes just result in a slow decay of intra-pair and inter-pair entanglements yet without destroying in-phase and anti-phase beating dynamics.
Resonant laser excitation of multiple Rydberg atoms are prohibited, leading to Rydberg blockade, when the long-range van der Waals interactions are stronger than the laser-atom coupling. Rydberg blockade can be violated, i.e., simultaneous excitation of more than one Rydberg atom, by off-resonant laser excitation, causing an excitation antiblockade. Rydberg antiblockade gives rise to strongly correlated many-body dynamics and spin-orbit coupling and also finds quantum computation applications. Instead of commonly used van der Waals interactions, we investigate antiblockade dynamics of two Rydberg atoms interacting via dipole-dipole exchange interactions. We study typical situations in current Rydberg atom experiments, where different types of dipole-dipole interactions can be achieved by varying Rydberg state couplings. An effective Hamiltonian governing underlying antiblockade dynamics is derived. We illustrate that geometric gates can be realized with the Rydberg antiblockade which is robust against the decay of Rydberg states. Our study may stimulate new experimental and theoretical exploration of quantum optics and strongly interacting many-body dynamics with Rydberg antiblockade driven by dipole-dipole interactions.
We report the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers. Working in a regime where the single-atom Rabi frequency for excitation to the Rydberg state is comparable to the interaction, we observe partial Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies. Quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and observe its characteristic C6/R6 dependence. The measured C6 coefficients agree well with ab initio calculations, and we observe their dramatic increase with the principal quantum number n of the Rydberg state.
Motivated by experimental advances that the collective excitation of two Rydberg atoms was observed, we provide an elaborate theoretical study for the dynamical behavior of two-atom Rabi oscillations. In the large-intermediate-detuning case, the two-photon Rabi oscillation is found to be significantly affected by the strength of the interatomic van der Waals interaction. With a careful comparison of the exact numbers and values of the oscillation frequency, we propose a new way to determine the strength of excitation blockade, agreeing well with the previous universal criterion for full, partial, and no blockade regions. In the small-intermediate-detuning case, we find a blockade-like effect, but the collective enhancement factor is smaller than 2 due to the quantum interference of double optical transitions involving the intermediate state. Moreover, a fast two-photon Rabi oscillation in ns timescale is manifested by employing intense lasers with an intensity of ∼ MW/cm 2 , offering a possibility of ultrafast control of quantum dynamics with Rydberg atoms.
We report the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers.Working in a regime where the single-atom Rabi frequency for excitation to the Rydberg state is comparable to the interaction, we observe partial Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies.Quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and observe its characteristic C 6 =R 6 dependence.The measured C 6 coefficients agree well with ab initio calculations, and we observe their dramatic increase with the principal quantum number n of the Rydberg state.
We report on the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers. By working in a regime where the single-atom Rabi frequency of the laser used for excitation to the Rydberg state is comparable to the interaction energy, we observe a \emph{partial} Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies. A quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and to observe its characteristic C6/R6C_6/R^6C6​/R6 dependence. The magnitude of the measured C6C_6C6​ coefficient agrees well with an \emph{ab-initio} theoretical calculation, and we observe its dramatic increase with the principal quantum number nnn of the Rydberg state. Our results not only allow to test an important physical law, but also demonstrate a degree of experimental control which opens new perspectives in quantum information processing and quantum simulation using long-range interactions between the atoms.