Quantum optics in 1D atoms

Exploring light-matter interaction at the single photon level is a quest of quantum optics, that has been successfully achieved so far with emitters in microwave or optical cavities. In such systems high atom-field couplings are obtained by trapping light in high quality factor resonators. Recently, alternative strategies have emerged, based on the broadband coupling of the emitter to a one-dimensional (1D) electromagnetic environment. These new devices invite to revisit important results of quantum optics, when the emitter interacts with propagating photons. We have studied the optical response of such one-dimensional atom when it is excited with a monochromatic classical pump. Going to the fully quantized picture, we have investigated the dynamics of an initially inverted atom in a waveguide in the presence of a single propagating photon. This works sheds new light on the physics of stimulated emission and opens the path to appealing applications for integrated quantum information and communication processing.

Fig.1 : a photonic wire is a typical candidate of a one-dimensional atom. bout and bin are the reflected and exciting light respectively.

Coupling a single atom to a single direction of the EM field was initially envisioned with the aim to perform quantum computation with single photons, which were acting as flying qubits. A pioneering realization of such a 1D atom consisted in an atom weakly coupled to a leaky cavity. Nowadays, 1D atoms can be implemented in a wide range of solid-state systems, from quantum dots embedded in photonic wires (fig.1 and [1]), in photonic crystals or in plasmonic waveguides to superconducting qubits in circuit QED. When probed with a resonant field, the natural directionality of 1D atoms allows to reach a high mode matching between the incoming and the scattered light, manifested by the destructive interference of the two fields. Equivalently, perfect mode matching allows to saturate the emitter with a single photon, so as 1D atoms have been identified as promising single photon transistors and two-photon gates.

We have investigated the signatures of this giant non-linear behavior when the atomic population is inverted, and revisited in the one-dimensional geometry the concept of stimulated emission [2]. Namely, we have analytically computed the dynamics of the 1D atom when the initially inverted emitter is impinged by a quantized propagating field. When it is properly shaped, a single resonant photon can shorten the atomic lifetime by a factor 2, leading to significant bunching in the output light field. Such an optimal irreversible stimulated emission corresponds to usual Einstein picture, and is actually a brand new phenomenon that can only been observed with 1D atoms. Indeed, in a monomode cavity, stimulation by a single photon is either optimal but reversible (if the atom is strongly coupled to the mode), or is irreversible (if the atom-field coupling is weak), but not optimal.

Fig. 2 : An initially inverted two-level atom is stimulated by a single pulsed-shape photon.

When the atom interacts with two 1D electromagnetic fields [3], preferential emission takes place in the mode excited with a single photon. We have shown that if stimulation is optimal, emission in the stimulated mode is twice more probable than in the empty mode. This property can be exploited to achieve efficient amplification of classical or quantum photonic states. For instance, an excited two-level atom in a transmitting waveguide behaves as an ultimate gain medium, emitting preferentially in the direction of the impinging photon. In the same way, an inverted lambda shaped three level atom in a semi-infinite waveguide can amplify the polarisation of a stimulating photon, allowing to achieve universal quantum cloning. This device is remarkable as the fidelity of the clones is maximal as in a cavity, but the clones are now free to propagate, a highly desirable property for all practical purposes. Moreover, depending on the spectral shape of the incoming photon, the device operates either as a deterministic source of entangled pairs of photons, or as an optimal cloning machine. This versatile behavior is the fruit of the broadband character of 1D atoms. It gives a glimpse of the richness of these systems which open a new and promising field for quantum optics and quantum information.

[1] "A highly efficient single-photon source based on a quantum dot in a photonic nanowire", J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.M.Gérard, Nature Photonics 4, 174 (2010).

[2] "Irreversible Optimal Stimulated Emission", D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, K. L. Chuan, M. F. Santos, A. Auffèves, New J. Phys. 14, 083029 (2012).

[3] Universal optimal photon cloning and entanglement creation in one-dimensional atoms, A. Auffèves, D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, K. L. Chuan, M. F. Santos, Phys. Rev. A 86, 022333 (2012).

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