E. del Valle

Collective fluid dynamics of a polariton condensate in a semiconductor microcavity

Semiconductor microcavities offer unique systems in which to investigate the physics of weakly interacting bosons. Their elementary excitations, polaritons—mixtures of excitons and photons—can accumulate in macroscopically degenerate states to form various types of condensate in a wide range of experimental configurations, under either incoherent or coherent excitation. Condensates of polaritons have been put forward as candidates for superfluidity, and the formation of vortices as well as elementary excitations with linear dispersion are actively sought as evidence to support this. Here, using a coherent excitation triggered by a short optical pulse, we have created and set in motion a macroscopically degenerate state of polaritons that can be made to collide with a variety of defects present in the microcavity. Our experiments show striking manifestations of a coherent light–matter packet, travelling at high speed (of the order of one per cent of the speed of light) and displaying collective dynamics consistent with superfluidity, although one of a highly unusual character as it involves an out-of-equilibrium dissipative system. Our main results are the observation of a linear polariton dispersion accompanied by diffusionless motion; flow without resistance when crossing an obstacle; suppression of Rayleigh scattering; and splitting into two fluids when the size of the obstacle is comparable to the size of the wave packet. This work opens the way to the investigation of new phenomenology of out-of-equilibrium condensates.eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website.

Emitters of N-photon bundles

Controlling the ouput of a light emitter is one of the basic tasks of photonics, with landmarks such as the laser and single-photon sources. The development of quantum applications makes it increasingly important to diversify the available quantum sources. Here, we propose a cavity QED scheme to realize emitters that release their energy in groups, or “bundles” of N photons, for integer N. Close to 100% of two-photon emission and 90% of three-photon emission is shown to be within reach of state of the art samples. The emission can be tuned with system parameters so that the device behaves as a laser or as a N-photon gun. The theoretical formalism to characterize such emitters is developed, with the bundle statistics arising as an extension of the fundamental correlation functions of quantum optics. These emitters will be useful for quantum information processing and for medical applications.

Theory of frequency-filtered and time-resolved N-photon correlations.

A theory of correlations between N photons of given frequencies and detected at given time delays is presented. These correlation functions are usually too cumbersome to be computed explicitly. We show that they are obtained exactly through intensity correlations between two-level sensors in the limit of their vanishing coupling to the system. This allows the computation of correlation functions hitherto unreachable. The uncertainties in time and frequency of the detection, which are necessary variables to describe the system, are intrinsic to the theory. We illustrate the power of our formalism with the example of the Jaynes-Cummings model, by showing how higher order photon correlations can bring new insights into the dynamics of open quantum systems.

Ultrafast Control and Rabi Oscillations of Polaritons

We report the experimental observation and control of space and time-resolved light-matter Rabi oscillations in a microcavity. Our setup precision and the system coherence are so high that coherent control can be implemented with amplification or switching off of the oscillations and even erasing of the polariton density by optical pulses. The data are reproduced by a quantum optical model with excellent accuracy, providing new insights on the key components that rule the polariton dynamics.

Generation of a two-photon state from a quantum dot in a microcavity

We propose and characterize a two-photon (2P) source that emits in a highly polarized, monochromatic and directional beam, realized by means of a quantum dot embedded in a linearly polarized cavity. In our scheme, the cavity frequency is tuned to half the frequency of the biexciton (two excitons with opposite spins) and largely detuned from the excitons thanks to the large biexciton binding energy. We show how the emission can be Purcell enhanced by several orders of magnitude into the 2P channel for available experimental systems.

Dynamics of the Formation and Decay of Coherence in a Polariton Condensate

We study the dynamics of the formation and decay of a condensate of microcavity polaritons. We investigate the relationship among the number of particles, the emission linewidth, and its degree of linear polarization, which serves as the order parameter. Tracking the condensate formation, we show that coherence is not determined only by occupation of the ground state, bringing new insights into the determining factors for Bose-Einstein condensation.

Mollow Triplet under Incoherent Pumping

Mollow [1] discovered a striking type of spectral shape in the resonance fluorescence problem, where an atom is irradiated by a strong laser beam. The celebrated Mollow triplet [2], that results from transitions between atomic states that are dressed by the coherent light field, has since been a testbed of nonlinear optics. It stands as one of the fundamental spectral shapes of lightmatter interaction, maybe second only to the Rabi doublet. Although the Mollow triplet is rooted in quantum physics and bears much quantum features itself, it arises from a fully classical light field. Its Hamiltonian, in the rotating frame of the laser and at resonance, simply reads HL = ΩL(σ + σ †), with ΩL the laser intensity and σ the only quantum operator, namely, the two-level system annihilation operator. Including the spontaneous decay of the emitter, in the Lindblad form Lσ(ρ) = (2σρσ† − σ†σρ− ρσ†σ), leads to a master equation ∂tρ = i[ρ,HL]+ γσ 2 Lσ(ρ) from which one obtains the famous Mollow triplet lineshape:

Effect of pure dephasing on the Jaynes-Cummings nonlinearities

We study the effect of pure dephasing on a two-level system in strong coupling in the nonlinear regime with the single mode of a cavity. The photoluminescence spectrum of the cavity has a robust tendency to display triplet structures, instead of the expected Jaynes-Cummings pairs of doublets at the incommensurate frequencies +/- (square root n +/- square root (n-1)) for integer n. We discuss recent experimental works that may already manifest signatures of single photon nonlinearities.

Spontaneous, collective coherence in driven, dissipative cavity arrays

We study an array of dissipative tunnel-coupled cavities, each interacting with an incoherently pumped two-level emitter. For cavities in the lasing regime, we find correlations between the light fields of distant cavities, despite the dissipation and the incoherent nature of the pumping mechanism. These correlations decay exponentially with distance for arrays in any dimension but become increasingly long ranged with increasing photon tunneling between adjacent cavities. The interaction-dominated and the tunneling-dominated regimes show markedly different scaling of the correlation length which always remains finite due to the finite photon trapping time. We propose a series of observables to characterize the spontaneous build-up of collective coherence in the system.

Luminescence spectra of quantum dots in microcavities. III. Multiple quantum dots

The coherent coupling of a semiconductor quantum dot (QD) exciton to the optical mode of a microcavity has been intensely investigated throughout the last years in cavity quantum electrodynamics (CQED) experiments [1–20] and theory [21–40]. In some of these works, the experimental spectral function of the strongly coupled QD–cavity system was directly compared to a theoretical model [11, 12, 19, 23], and the agreement is excellent. It was assumed that most of the light escapes the system via the radiation pattern of the cavity mode, and the experimental spectra were compared to the spectral function calculated from the cavity occupation. This detection geometry is known in atomic cQED as “end emission” or “forward emission” [41]. In atomic systems, negligible light escapes the cavity through the cavity mode, that is to say, the cavity photon lifetime is so long as to be considered infinite. Light is then detected in the so-called “side-emission”, where the radiation pattern of the emitter is probed instead. With microcavities, the situation is reversed: the cavity mode is measured often with an emitter of a much longer lifetime. In the spontaneous emission regime of a system in strong-coupling, this makes measurements of the Rabi doublet in the photoluminescence more difficult, unless some cavity feeding makes the quantum state of the system photon-like, since changing the nature of the excitation is, in this case, equivalent to changing the channel of detection [23]. In the nonlinear regime, this also hinders manifestations of the Jaynes–Cummings ladder. All the transitions between its rungs have the same intensity in the exciton emission. In the cavity emission, however, the photon has two paths to be emitted, one with the dot in its ground state, the other with the dot in its excited states [28]. These two paths interfere destructively when the initial and final states are out of phase, which is the case for two out of the four possible transitions in the Jaynes–Cummings ladder. On the other hand, these two paths interfere constructively when the initial and final states are in phase, or, up to a photon, indistinguishable. In the dressed-state picture, the cavity photon to be emitted decouples from the polaritons and carries away little information from the coupled system, being more like a cavity photon the higher the number of excitations. The dot photon, on the other hand, does not decouple from the system, regardless the number of excitations: the dot cannot de-excite without altering fundamentally the state of the entire system. As a result, the dot photon carries more information of the coupled system. Summarizing, the dot is essentially a quantum emitter whereas the cavity is essentially a classical emitter. It is therefore interesting to detect directly the dot emission. The ratio R of dot-vs-cavity emitted photons depends on the populations of the dot (resp. cavity), n1 (resp. na) and their rate of emission, γ1 (resp. γa):