Cooperative Effects in Closely Packed Quantum Emitters with Collective Dephasing

Abstract

In a closely packed ensemble of quantum emitters, cooperative effects are typically suppressed due to the dephasing induced by the dipole-dipole interactions. Here, we show that by adding sufficiently strong collective dephasing cooperative effects can be restored. In particular, we show that the dipole force on a closely packed ensemble of strongly driven two-level quantum emitters, which collectively dephase, is enhanced in comparison to the dipole force on an independent non-interacting ensemble. Our results are relevant to solid state systems with embedded quantum emitters such as colour centers in diamond and superconducting qubits in microwave cavities and waveguides. A collection of two-level quantum emitters (TLEs) with sub-wavelength average separations can show remarkable cooperative behaviour like superradiant emission [1][2][3]. The study of optical response in such systems has predominantly been restricted to the emission properties or the propagation of light within the TLE ensemble. This is because the systems usually considered in the early days [2,4], as well as in some recent works [5][6][7][8], are gaseous clouds of atoms. With the advent of artificial atoms in solid state systems, e.g. quantum dots [9], superconducting qubits [10,11] and colour centers in diamond [12][13][14], it is now possible to study the impact of cooperative effects on other aspects of the optical response. In particular, a recent experiment [13] studied the dipole force on optically trapped nanodiamonds containing a high density of Nitrogen vacancy (NVs) centers. An intriguing result in [13] was that the observed dipole force originating from the emitters could not be correctly accounted for by considering the emitters to respond independently.In this work, we focus on cooperative effects in a small and closely packed ensemble of TLEs subject to strong coherent driving and collective dephasing. In particular, we show that the dipole force on such an ensemble can be larger than on an equivalent one where each TLE spontaneously emits independently. For the emitter separations that we consider here, the dipole-dipole interaction can be larger than the line-width of the individual emitters. Furthermore, spontaneous emission is not perfectly collective. In this situation, one typically expects cooperative effects to be suppressed [2,15]. Here, we show that the combination of strong driving and large collective dephasing can restore cooperative effects, even in the presence of dipole interaction shifts and non-collective spontaneous emission. While there have been previous studies of cooperative effects with strong driving fields [16][17][18][19][20][21][22], the role of collective dephasing has received less attention [10,13]. In the context of Quantum Information, collective decoherence in general, and collective dephasing in particular, has been studied both theoretically [23][24][25] and experimentally [26,27]. There, particular attention was paid to the existence and robustness of so called decoherence free sub-spaces (D...

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