Quantum nonlinear optics without photons

Abstract

Spontaneous parametric down-conversion is a well-known process in quantum nonlinear optics in which a photon incident on a nonlinear crystal spontaneously splits into two photons. Here we propose an analogous physical process where one excited atom directly transfers its excitation to a pair of spatially-separated atoms with probability approaching one. The interaction is mediated by the exchange of virtual rather than real photons. This nonlinear atomic process is coherent and reversible, so the pair of excited atoms can transfer the excitation back to the first one: the atomic analog of sum-frequency generation of light. The parameters used to investigate this process correspond to experimentally-demonstrated values in ultrastrong circuit quantum electrodynamics. This approach can be extended to realize other nonlinear interatomic processes, such as four-atom mixing, and is an attractive architecture for the realization of quantum devices on a chip. We show that four-qubit mixing can efficiently implement quantum repetition codes and, thus, can be used for error-correction codes.arXiv:1702.00660v2 [quant-ph] 24 Aug 2017 0 0.6 |g, e, e, gi |g, e, g, ei |g, g, e, ei | e , g , g , e i | e , g , e , g i | e , e , g , g i | e , g , e , g i | e , e , g , g i |g, g, g, ei |g, g, e, gi |g, e, g, gi | e , g , g , g i |g, e, g, gi

Circuit QED with qutrits: Coupling three or more atoms via virtual-photon exchange

“…(q = 2, 3) almost coincide at early time [27]. This is a signature of almost perfect two-atom correlation: if one atom is excited, the other is also excited [31].…”

“…This process can be exploited for the realization of an efficient atom-atom entanglement source [27,46] and can also be used for the implementation of novel schemes for the control and manipulation of atom states, e.g., three-qubit gates [48], quantum repetition coding [27] needed for error-correction codes. Furthermore, it is also possible to use the photonmediated multi-atom interaction to engineer long-distance entangled state and stabilization of pure many-body states of atoms [49].…”

“…Recently, Stassi et al [27] have theoretically demonstrated that the interaction of multiple spatially-separated atoms can be realized via the exchange of virtual photons in the ultrastrong-coupling (USC) regime of cavity quantum electrodynamics [28]. In the USC regime, the atom-cavity coupling strength is comparable to the atom and cavity energy scales.…”

“…Therefore, Eq. (4) provides a approach to coupling three or more atoms via a cavity bus [27]. Moreover, when frequency matching condition is satisfied, i.e., ω…”

“…e , the n atoms (qth atom, q = 2, .., n + 1) can conspire to jointly exchange excitation with the 1st atom, which implies a resonant interaction among the multiple atoms via the exchange of virtual photons [27]. This process is enabled by the resonant transitions between the bare states |0, e, g, ..., g and |0, g, e, ..., e , with an example shown in Fig.…”