Temperature dependence of the coherence in polariton condensates

We present a time-resolved experimental study of the temperature effect on the coherence of traveling polariton condensates. The simultaneous detection of their emission both in real and reciprocal space allows us to fully monitor the condensates’ dynamics. We obtain fringes in reciprocal space as a result of the interference between polariton wave packets (WPs) traveling with the same speed. The periodicity of these fringes is inversely proportional to the spatial distance between the interfering WPs. In a similar fashion, we obtain interference fringes in real space when WPs traveling in opposite directions meet. The visibility of both real- and reciprocal-space interference fringes rapidly decreases with increasing temperature and vanishes. A theoretical description of the phase transition, considering the coexistence of condensed and noncondensed particles, for an out-of-equilibrium condensate such as ours is still missing, yet a comparison with theories developed for atomic condensates allows us to infer a critical temperature for the BEC-like transition when the visibility goes to zero.

Figure 1

(a) PL emission along the ridge in real space ($x$) as a function of time for $T=14\mathrm{K}$. ${\mathrm{S}}_{1,2}$ mark the positions where the two laser beams impinge on the sample. ${\mathrm{L}}_i\left({\mathrm{R}}_i\right)$ denote the WPs moving to the left (right), with the subscript, $i$, referring to the excitation beam. The red dashed arrow at the top of the image represents the spatial separation ($d$) between both beams at $t=0$ while the arrow at $\sim 55\mathrm{ps}$ marks the separation ($d_2$) between WPs ${\mathrm{R}}_1$ and ${\mathrm{L}}_2$ when they arrive at the excitonic reservoirs. The intensity is in a linear false-color scale. (b) The corresponding emission in momentum space ($k$) as a function of time. The color of the arrows refers to the WPs described in (a). In this case, the intensity is in a logarithmic false-color scale. Both PL emissions have been measured with a power density of $6\mathrm{kW}/\mathrm{c}{\mathrm{m}}^2$.

Figure 2

(a) PL emission in momentum space, time integrated for $t_1$ at a temperature of 10 K. (b) Interferogram profile after a baseline subtraction of the trace shown in (a). (c) Amplitude of the different contributions to the interferogram obtained from a Fourier analysis of the trace depicted in (b): The value of the main period of the interference fringes is marked as ${\kappa }_0$, the corresponding visibility as $v$. The dashed line shows a Bézier interpolation of the points. A $10\mathrm{kW}/\mathrm{c}{\mathrm{m}}^2$ excitation laser was used in the measurements.

Figure 3

Profile of the emission spectra for $t_1$ in momentum space varying the temperature from 10 K (top) to 35 K (bottom) in steps of 2.5 K (only the first and last three temperatures are labeled).

Figure 4

Temperature dependence of the visibility of the interference fringes: in momentum space for the interval $t_1$ (black), in the vicinity of $k=0$ at $t_3$ (blue), and in real space at the first crossing of the wave packets, ${\mathrm{R}}_1$ and ${\mathrm{L}}_2$, $t_2$ (red). The inset shows the fraction of condensed to uncondensed polariton populations ($f_C$) for increasing temperatures during the time interval $t_1$. The lines represent fits of the data with $v\left(\mathrm{T}\right)=v_0\left[1-{\left(\mathrm{T}/{\mathrm{T}}_{\mathrm{C}}\right)}^{\beta }\right]$, for $\beta =1$ (dotted line) and $\beta =3$ (solid line).