Two-Photon Dynamics in Coherent Rydberg Atomic Ensemble

Abstract

We study the interaction of two photons in a Rydberg atomic ensemble under the condition of electromagnetically induced transparency, combining a semi-classical approach for pulse propagation and a complete quantum treatment for quantum state evolution. We find that the blockade regime is not suitable for implementing photon-photon cross-phase modulation due to pulse absorption and dispersion. However, approximately ideal cross-phase modulation can be realized based on relatively weak interactions, with counter-propagating and transversely separated pulses.Strong nonlinearity at the single-photon level is desirable to the realization of all-optical quantum devices. Ensembles of highly excited Rydberg atoms under electromagnetically induced transparency (EIT) condition combine the advantages of strong atom-field coupling without significant absorption and non-local atomic interaction, and have attracted intensive experimental [1][2][3][4][5][6][7] and theoretical studies [8][9][10][11][12][13][14][15][16][17] recently. The strong correlation directly between single photons inside Rydberg atomic ensemble was observed [7], and the formation of a Wigner crystal of individual photons is also predicted [15]. When such interaction is applied to implement the cross-phase modulation (XPM) between two individual photons with a non-zero relative velocity as in Fig. 1 [18-21], a main difference from a single probe beam propagation in Rydberg EIT medium [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] is that no steady state exists for the pulses, because their interaction varies with the relative distance, pulse velocity that changes pulse sizes, as well as the absorption in medium. The realistic timedependence in the inherent nonlinear dynamics makes a complete solution of the problem rather challenging. With the combination of a semi-classical approach for pulse propagation and a complete quantum approach for pulse quantum state evolution, we find a realistic picture for the dynamical process by showing the concerned figures of merit. We show that our proposed setup outperforms the previously considered Rydberg blockade regime [20] clearly in terms of much lower photon absorption and negligible group velocity dispersion.The detailed two-photon XPM via Rydberg EIT is as follows. One respectively couples the far-away input photons to cold Rydberg atoms under the EIT condition to form the light-matter quasi-particle called darkstate polariton (DSP) [22]. The spatial distribution of the pulses necessitates a quantum many-body description of the process. The prepared DSPs are in the state |1 l

Nonlinear optical signals and spectroscopy with quantum light

“…Recent advances in quantum optics extend nonlinear signals down to the few-photon level where the quantum nature of the field is manifested, and must be taken into account: The enhanced light-matter coupling in cavities (Raimond et al, 2001;Schwartz et al, 2011;Walther et al, 2006), the enhancement of the medium's nonlinearity by additional driving fields (Chen et al, 2013;Peyronel et al, 2012), large dipoles in highly excited Rdberg states (Gorniaczyk et al, 2014;He et al, 2014), molecular design (Castet et al, 2013;Loo et al, 2012), or strong focussing (Faez et al, 2014;Pototschnig et al, 2011;Rezus et al, 2012) all provide possible means to observe and control nonlinear optical processes on a fundamental quantum level. Besides possible technological applications such as all-optical transistors (Shomroni et al, 2014) or photonic quantum information processing (Braunstein and Kimble, 2000;Franson, 1989;Jennewein et al, 2000;Knill et al, 2001;Kok et al, 2007;O'Brien et al, 2003;U'Ren et al, 2003), these also show great promise as novel spectroscopic tools.…”

Intracavity Rydberg-atom electromagnetically induced transparency using a high-finesse optical cavity

“…A number of review articles exist on various specific topics, e.g., Rydberg atom interactions [4,5], quantum information with Rydberg atoms [6,7], Rydberg atoms in magnetic fields [8] and microwave field sensing with Rydberg atoms [9]. New experiments and theory, where collective Rydberg excitations created in ultracold gases are used to shape electro-magnetic fields at the quantum level, are beginning to attract increasing attention [10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Photon-photon gate via the interaction between two collective Rydberg excitations

“…There is a significant body of work studying the effects of mapping photons onto collective atomic Rydberg excitations [14][15][16][17][18][19][20]. Most proposals for photon-photon gates involve propagating Rydberg excitations (polaritons), either using blockade [21,22] or two excitations [23][24][25][26].…”

“…Achieving blockade conditions can be challenging since both photons have to be localized within the blockade volume. Following [6,7,[23][24][25][26], we here propose a storage-based scheme that instead relies on the interaction between two stationary Rydberg excitations.The main challenge for two-excitation based Rydberg gates in atomic ensembles arises from the fact that the interaction is strongly distance-dependent and thus not uniform over the profiles of the two stored photons. We show that this a priori reduces the gate's fidelity by displacing the collective excitations in momentum space and by entangling their quantum states.…”

“…Achieving blockade conditions can be challenging since both photons have to be localized within the blockade volume. Following [6,7,[23][24][25][26], we here propose a storage-based scheme that instead relies on the interaction between two stationary Rydberg excitations.…”