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From Single Particle to Superfluid Excitations in a Dissipative Polariton Fluid

Excitons-polaritons are the elementary bosonic excitations of semiconductor microcavity in the so-called strong coupling regime. Owing to their bosonic and interacting nature, and in spite of their driven-dissipative nature, polaritons are found to exhibit superfluid behavior. As pointed out by Bogoliubov in his celebrated theory of superfluidity, the phenomena of superfluidity arises from a profound transformation of the nature of the excitations of the system, at the normal to superfluid transition. Using a non-linear optical spectroscopic technique, we observed directly this transformation, and reported for the first time an experimental measurement of the polariton superfluid linear dispersion, reminiscent of sound wave excitation (sometime referred to as zero sound), accompanied by a characteristic lower energy anomalous dispersion branch.

The first observation of superfluidity has been reported in helium II by Kapitza and Allen and Misener. This intriguing finding triggered a feverish theoretical activity to understand the physics of quantum fluids. London quickly linked superfluidity with Bose-Einstein condensation, stressing the importance of the bosonic nature of the particles. Meanwhile, Landau developed the idea of sound-like excitations as being the elementary excitations of a superfluid. These intuitions were later confirmed by Bogoliubov, whose microscopic theory of weakly interacting Bose gas provides a clear explanation of the reported properties of superfluid. In this regime the excitations dispersion deviates substantially from the parabolic single particle case. It turns linear in its low energy part and the corresponding elementary excitations (formally described as particle-hole excitations) thus resembles sound waves. In addition to the normal positive energy branch (NB), the theory predicts the coexistence of another dispersion branch at negative energy (with respect to the superfluid rest energy) resulting from the hole component of the excitation. The linear normal and anomalous dispersion branches are mirror image of each other and represent the expected dispersion of a superfluid. The direct measurement of Bogoliubov dispersion is a difficult task, as it requires both energy and momentum measurements of the elementary excitations on top of the superfluid.

Figure 1
a) Four wave mixing spectrum for different trigger pulse wave-vector. The high energy peak corresponds to an excitation in the normal branch, the low energy one correspond to an excitation in the anomalous branch. b) Reconstructed dispersion : the red dots are the measured dispersion. The dashed line shows the single particle parabolic dispersion for comparison. The grayscale figure is the calculated Bogoliubov dispersion.

Polaritons are Bosonic excitations of semiconductor microcavities in the strong coupling regime. They are half-light half-exciton in nature. The latter is responsible for weak interactions between polaritons, while the earlier is responsible for a short lifetime, and also provides a unique opportunity to a full optical access to the dispersion of the elementary excitations in the superfluid regime.

To do so [1] we used a non-linear optical spectroscopy technique known as Four-wave-mixing (FWM). Two ultra-short pulses of light are used to excite and probe the superfluid. The first one creates the superfluid at zero momentum, while the second one creates an elementary excitation in it at a well-defined wave-vector kt. This trigger pulse stimulates the generation of another excitation at opposite wave-vector kFWM=-kt which is then collected by angle selective detection of the emission plus a spectral heterodyning technique. The corresponding signal is shown in Fig.1.a for different kt while in the superfluid regime. Two peaks clearly appear, the upper one corresponds to the “particle” part of the Bogoliubov excitation (i.e. on the normal dispersion branch), while the lower one correspond to the “hole” part (i.e. on the anomalous dispersion branch). In this way the full dispersion of the polariton superfluid excitations can be reconstructed, the result is shown in Fig.1.b. As expected, we obtain an unambiguously linear dispersion of the normal branch as well as the appearance of an anomalous branch at low energy. From the measured linear dispersion we could infer the sound velocity within the superfluid, which amounts to 0.2% of the speed of light. This ultra-large sound speed is mainly a consequence of the very light mass of polaritons. The dissipative nature of the polariton superfluid also modifies slightly the usual equilibrium superfluid picture. It is for example responsible for the peculiar dispersion shape of the anomalous branch. The latter is well accounted for by a mean-field calculation taking dissipation into account.

This measurement constitutes the first unambiguous demonstration that a Bogoliubov transformation occurs at the transition from a normal to superfluid phase in a polariton gas.

[1] “From single particle to superfluid excitations in a dissipative polariton gas”, V. Kohnle, Y. Léger, M. Wouters, M. Richard, M.T. Portella- Oberli and B. Deveaud, Phys. Rev. Lett. 106 255302 (2011).

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