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arXiv:1901.09265 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamics and quantum correlations in two independently driven Rydberg atoms with distinct laser fields

Vineesha Srivastava, Ankita Niranjan, Rejish Nath

Published Jul 17, 2019• 7 citations
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Abstract

Abstract We study the population dynamics in a two-atom setup in which each atom is driven independently by different light fields, but coupling the same Rydberg state. In particular, we look at how an offset in the Rabi frequencies between two atoms affects the dynamics. We find novel features such as amplifying the Rabi frequency of one atom, together with strong Rydberg-Rydberg interactions freezes the dynamics in the second atom. We analyze this Rydberg-biased freezing phenomenon in detail, with effective Hamiltonians obtained for various limits of the system parameters. In the absence of Rabi-offset, the doubly excited state population exhibits a Lorentzian profile as a function of interaction, whereas for very small offsets it shows splitting and thus peaks. Using an effective Hamiltonian, as well as the perturbation theory in the weak interaction limit, we show that the peak arises from a competition between Rabi-offset and Rydberg-Rydberg interactions when both are sufficiently small, together with the Rydberg blockade at large interactions. The effective Hamiltonians provide us with analytical results for long time dynamics, which are in an excellent agreement with exact numerical solutions. Also, we analyze the growth and the dynamics of quantum correlations such as entanglement entropy/quantum discord for the coherent dynamics. Finally, we extend our studies to the dissipative case in which the spontaneous emission from the Rydberg state is taken into account and in particular, we look at how the Rabi-offset modifies the purity and quantum discord in the steady states. We conclude that the local manipulation of an atom by introducing a Rabi-offset can be a useful tool to control the quantum correlations and in general, the quantum states of the composite two-qubit systems.

DOI
10.1088/1361-6455/ab32a2

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Abstract We study the population dynamics in a two-atom setup in which each atom is driven independently by different light fields, but coupling the same Rydberg state. In particular, we look at how an offset in the Rabi frequencies between two atoms affects the dynamics. We find novel features such as amplifying the Rabi frequency of one atom, together with strong Rydberg-Rydberg interactions freezes the dynamics in the second atom. We analyze this Rydberg-biased freezing phenomenon in detail, with effective Hamiltonians obtained for various limits of the system parameters. In the absence of Rabi-offset, the doubly excited state population exhibits a Lorentzian profile as a function of interaction, whereas for very small offsets it shows splitting and thus peaks. Using an effective Hamiltonian, as well as the perturbation theory in the weak interaction limit, we show that the peak arises from a competition between Rabi-offset and Rydberg-Rydberg interactions when both are sufficiently small, together with the Rydberg blockade at large interactions. The effective Hamiltonians provide us with analytical results for long time dynamics, which are in an excellent agreement with exact numerical solutions. Also, we analyze the growth and the dynamics of quantum correlations such as entanglement entropy/quantum discord for the coherent dynamics. Finally, we extend our studies to the dissipative case in which the spontaneous emission from the Rydberg state is taken into account and in particular, we look at how the Rabi-offset modifies the purity and quantum discord in the steady states. We conclude that the local manipulation of an atom by introducing a Rabi-offset can be a useful tool to control the quantum correlations and in general, the quantum states of the composite two-qubit systems.
Interaction between Rydberg atoms can significantly modify Rydberg excitation dynamics. Under a resonant driving field the Rydberg-Rydberg interaction in high-lying states can induce shifts in the atomic resonance such that a secondary Rydberg excitation becomes unlikely leading to the Rydberg blockade effect. In a related effect, off-resonant coupling of light to Rydberg states of atoms contributes to the Rydberg anti-blockade effect where the Rydberg interaction creates a resonant condition that promotes a secondary excitation in a Rydberg atomic gas. Here, we study the light-matter interaction and dynamics of off-resonant two-photon excitations and include two- and three-atom Rydberg interactions and their effect on excited state dynamics in an ensemble of cold atoms. In an experimentally-motivated regime, we find the optimal physical parameters such as Rabi frequencies, two-photon detuning, and pump duration to achieve significant enhancement in the probability of generating doubly-excited collective atomic states. This results in large auto-correlation values due to the Rydberg anti-blockade effect and makes this system a potential candidate for a high-purity two-photon Fock state source.
The excitation dynamics of a laser-driven Rydberg-atom system exhibits a cooperative effect due to the interatomic Rydberg-Rydberg interaction, but the large many-body system with inhomogeneous Rydberg coupling is hard to exactly solve or numerically study by density-matrix equations. In this paper, we find that the laser-driven Rydberg-atom system with most of the atoms being in the ground state can be described by a simplified interaction model resembling the optical Kerr effect if the distance-dependent Rydberg-Rydberg interaction is replaced by an infinite-range coupling. We can then quantitatively study the effect of the quantum fluctuations on the Rydberg excitation with the interatomic correlation involved and analytically calculate the statistical characteristics of the excitation dynamics in the steady state, revealing the quantum signature of the driven-dissipative Rydberg-atom system. The results obtained here will be of great interest for other spin-1/2 systems with spin-spin coupling.
We consider two two-level atoms fixed at different positions, driven by a monochromatic laser field, and interacting collectively with the vacuum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms and their steady-state is obtained analytically for two configurations, one in which the atoms are in equivalent positions and another in which they are not. The steady-state populations of the energy levels of the free atoms, entanglement, quantum discord and degree of mixed-ness are calculated analytically as a function of the laser field intensity and the distance between the two atoms. It is found that driving both atoms with the laser field is inefficient for the generation of steady-state correlations when they are in equivalent positions. On the contrary, inequivalent positions lead to the possibility of considerable steady-state entanglement and left/right quantum discord. It is shown that an X-state can be obtained for high laser field intensities for both configurations. This allows the comparison of two measures of quantum discord. The behaviour and relationships between correlations are studied and several limiting cases are investigated.
The interaction between atoms and a quantized radiation field is fundamentally important in quantum optics and quantum information science. Due to their unusual properties, Rydberg atoms are promising building blocks for two-qubit gates and atom-light quantum interfaces, exploiting the Rydberg blockade interaction which prevents two atoms at close distance ( < 10 μ m ) from being simultaneously excited to Rydberg states. Recently, this effect was used to engineer quantum processors based on arrays of interacting Rydberg atoms illuminated by Raman lasers. Motivated by these experiments, we extend the Jaynes–Cummings model to study the interaction between two Rydberg atoms interacting by the Rydberg blockade and a quantized radiation field. We consider both number (Fock) states of the field and single-mode quantum coherent states. In particular, we discuss different types of entanglements between various components of the total system consisting of the two Rydberg-interacting atoms and coherent states of the field, and show that the behavior is significantly different compared to a system with non-interacting atoms corresponding to the two-atom Tavis-Cummings model. Our results are relevant in view of atom-light quantum interfaces as components for future long-distance quantum communication.
We study the dynamics of up to two Rydberg excitations and the correlation growth in a chain of atoms coupled to a photonic crystal waveguide. In this setup, an excitation can hop from one atom to another via exponentially decaying exchange interactions mediated by the waveguide. An initially localized excitation undergoes a continuous-time quantum walk for short-range hopping, and for long-range hopping, it experiences quasilocalization. In addition, the inverse participation ratio reveals a superballistic diffusion of the excitation in short times, whereas, at a long time, it becomes ballistic. For two initially localized excitations, intriguing and complex dynamical scenarios emerge for different initial separations due to the competition between the Rydberg-Rydberg and exchange interactions. In particular, the two-point correlation reveals a light-cone behavior even for sufficiently long-range exchange interactions. Additionally, we characterize the growth of bipartite entanglement entropy, which exhibits a global bound if only one excitation is present in the dynamics. Finally, we analyze the effect of imperfections due to spontaneous emission from the Rydberg state into photons outside the waveguide and show that all of the physical phenomena we predict are well within experimental reach.
An array of single Rydberg atoms driven by a temporally modulated atom-field detuning is studied. The periodic modulation effectively modifies the Rabi coupling, leading to unprecedented dynamics in the presence of Rydberg-Rydberg interactions, in particular, blockade enhancement, antiblockades, and state-dependent population trapping. Interestingly, the Schrieffer-Wolf transformation reveals a fundamental process in Rydberg gases, correlated Rabi coupling, which stems from the extended nature of the Rydberg-Rydberg interactions. Also, the correlated coupling provides an alternative depiction for the Rydberg blockade, exhibiting a nontrivial behavior in the presence of periodic modulation. The dynamical localization of a many-body configuration in a driven Rydberg lattice is discussed.