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Physical Review A

Interplay of the dipole blockade and interaction-induced dephasing in Rydberg single-photon sources

P. R. Berman, A. Kuzmich

Published Jan 16, 2024• 4 citations
Publisher

Abstract

Interactions between Rydberg atoms can result in a dipole blockade for which the probability ${P}_{n}$ to have $n$ atomic excitations is reduced significantly when $n\ensuremath{\ge}2$. Ideally, this allows one to create a single collective Rydberg excitation in an atomic ensemble with ${P}_{1}=1$. A single-photon source is realized by mapping this atomic excitation into a propagating light field. Even if ${P}_{n}\ensuremath{\ne}0$ for $n\ensuremath{\ge}2$, a single-photon source can be approximated if interaction-induced dephasing damps the contributions from multiply excited collective states into the preferred spatial field mode. Two quantities that can be used as figures of merit for these single-photon sources are the second-order correlation function ${g}^{(2)}$ associated with the phase-matched field emitted by the sample and the second-order correlation function ${g}^{(A)}$ associated with the atoms. Here we demonstrate that interaction-induced dephasing can lead to significant differences between ${g}^{(2)}$ and ${g}^{(A)}$ even if ${P}_{2}\ensuremath{\ll}{P}_{1}\ensuremath{\approx}1$. Theoretical expressions are derived for these quantities and it is shown that ${g}^{(2)}\ensuremath{\le}{g}^{(A)}$. It is also shown that there is a distinct advantage for minimizing ${g}^{(2)}\phantom{\rule{4pt}{0ex}}$ and ${g}^{(A)}$ by using adiabatic pulsed fields rather than constant amplitude fields to excite the ensemble. These results maybe useful for optimizing Rydberg single-photon sources.

DOI
10.1103/physreva.109.013710

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Interactions between Rydberg atoms can result in a dipole blockade for which the probability Pn{P}_{n}Pn​ to have nnn atomic excitations is reduced significantly when n\ensuremath≥2n\ensuremath{\ge}2n\ensuremath≥2. Ideally, this allows one to create a single collective Rydberg excitation in an atomic ensemble with P1=1{P}_{1}=1P1​=1. A single-photon source is realized by mapping this atomic excitation into a propagating light field. Even if Pn\ensuremath≠0{P}_{n}\ensuremath{\ne}0Pn​\ensuremath=0 for n\ensuremath≥2n\ensuremath{\ge}2n\ensuremath≥2, a single-photon source can be approximated if interaction-induced dephasing damps the contributions from multiply excited collective states into the preferred spatial field mode. Two quantities that can be used as figures of merit for these single-photon sources are the second-order correlation function g(2){g}^{(2)}g(2) associated with the phase-matched field emitted by the sample and the second-order correlation function g(A){g}^{(A)}g(A) associated with the atoms. Here we demonstrate that interaction-induced dephasing can lead to significant differences between g(2){g}^{(2)}g(2) and g(A){g}^{(A)}g(A) even if P2\ensuremath≪P1\ensuremath≈1{P}_{2}\ensuremath{\ll}{P}_{1}\ensuremath{\approx}1P2​\ensuremath≪P1​\ensuremath≈1. Theoretical expressions are derived for these quantities and it is shown that g(2)\ensuremath≤g(A){g}^{(2)}\ensuremath{\le}{g}^{(A)}g(2)\ensuremath≤g(A). It is also shown that there is a distinct advantage for minimizing g(2){g}^{(2)}\phantom{\rule{4pt}{0ex}}g(2) and g(A){g}^{(A)}g(A) by using adiabatic pulsed fields rather than constant amplitude fields to excite the ensemble. These results maybe useful for optimizing Rydberg single-photon sources.
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.
We discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our calculations reproduce and interpret the results of recent experiments.
We propose an efficient free-space scheme to create single photons in a well-defined spatiotemporal mode. To that end, we first prepare a single source atom in an excited Rydberg state. The source atom interacts with a large ensemble of ground-state atoms via a laser-mediated dipole-dipole exchange interaction. Using an adiabatic passage with a chirped laser pulse, we produce a spatially extended spin wave of a single Rydberg excitation in the ensemble, accompanied by the transition of the source atom to another Rydberg state. The collective atomic excitation can then be converted to a propagating optical photon via a coherent coupling field. In contrast to previous approaches, our single-photon source does not rely on the strong coupling of a single emitter to a resonant cavity, nor does it require the heralding of collective excitation or complete Rydberg blockade of multiple excitations in the atomic ensemble.
Mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons enables the realization of optical nonlinearities which can modify light on the level of individual photons.This novel approach forms the basis of a growing Rydberg quantum optics toolbox, which already contains photonic logic building-blocks such as single-photon sources, switches, transistors, and conditional π-phase shifts.This thesis reports on two experiments investigating strong photon-photon interactions mediated by Rydberg interactions.First, applying a ladder-type EIT scheme to Rydberg atoms in D-states with high principal quantum number results in the Rydberg interaction mediated nonlinearity accompanied by a time-dependent decay of transmission of probe light through the medium.In a joint experimental and theoretical analysis, this effect is attributed to the dephasing of propagating polaritons into stationary Rydberg excitations caused by the state mixing interaction occurring with Rydberg D-state atoms.Second, via a two-photon Raman excitation scheme Rydberg atoms are efficiently excited in a small atomic cloud.As the size of the Rydberg blockade exceeds the dimension of the medium, only a single Rydberg excitation can be present at a time.By fast engineered dephasing this Rydberg excitation is decoupled from the light field.Measurement of the transmitted light and the amount of excited Rydberg atoms gives evidence for the realization of a deterministic single-photon absorber.
Based on the dipole blockade effect and with the aid of the superatom (SA) model, we propose a scheme to investigate the correlated evolution of two Rydberg sub-superatoms (SSAs), formed by two spatially separated atomic Rydberg sub-ensembles but in the same blockade region. Starting from the pure separable states, we investigate the in-phase or anti-phase correlated dynamics and explore how two Rydberg SSAs entangle with each other mediated by a single Rydberg excitation. Starting from the entangled states, we discuss the robustness of the system against decoherence induced by the dephasing rate. Our results show that both the correlated evolution of two Rydberg SSAs and their collective-state entanglement are usually sensitive to the number of each Rydberg SSA. This allows us to coherently manipulate the Rydberg ensemble over long distances from the single-quantum level to the mesoscopic level by changing the number of atoms. Furthermore, the method for dividing an SA into two SSAs and obtaining their spin operators without any approximation can be readily generalized to the case of many SSAs. It may have potential promising applications in quantum information processing and provide an attractive platform to study the quantum-classical correspondence, many-body physics and so on.
Owing to the unique physical characteristics of Rydberg atoms, which play an important role in quantum information and quantum computation, the theoretical and applied research of Rydberg atoms have become the hot spots of scientific research in recent years. With the large polarizability of Rydberg atoms, even a small electric field could cause a considerable electric dipole moment, resulting in a strong dipole-dipole interaction between Rydberg atoms. The multiple excitations of the Rydberg states are strongly inhibited because of the strong dipole interaction between atoms within a mesoscopic interaction (blockade) region. We call this phenomenon the dipole blockade effect. The dipole blockade effect makes it possible to build single-photon quantum devices, implement quantum gates, generate quantum entanglement, and simulate many-body quantum problems, etc. A Rydberg atomic ensemble in the same blockade region can be regarded as a superatom. In the same way, if these atoms trapped in two optical dipole traps, each sub-ensemble can be considered as a sub-superatom which is closely related to the superatom. According to the fact that two Rydberg sub-superatoms can be strongly correlated due to sharing no more than one excited Rydberg atom, we study correlated collective excitation and quantum entanglement between two Rydberg sub-superatoms in a steady state. With the superatom model, the problem of exponentially increasing system size with the number of atoms can be circumvented to a certain extent in studying many-body physics. By solving the two-body Lindblad’s master equation accurately, we obtain the analytical expressions for the collective excitation probabilities of the two sub-superatoms, and the concurrence measuring the bipartite entanglement between them. Our results show that they are all sensitive to the number of atoms in each Rydberg superatom: the bigger (including more atoms) the Rydberg superatom, the higher the collective Rydberg excitation probability is. And that the maximally entangled state can only be obtained with two equal-sized Rydberg superatoms. When this condition is fulfilled, the mesoscopic entanglement can be generated by adding the number of atoms in each Rydberg superatom. This may provide an attractive platform for studying the quantum-classical correspondence and have potential promising applications in quantum information processing.