Ultrafast dynamics of exciton–polariton in optically tailored potential landscapes at room temperature

In this section, potential wells with controlled widths are realized by changing the spatial separation between two laser beams. Polariton harmonic oscillators with various highest excited SHO (simple harmonic oscillator) states characterized by different node numbers are obtained. In the non-resonant excitation regime, exciton reservoir is firstly generated by femtosecond injection, which undergoes effective cooling [29]. The two exciton reservoirs perform essentially as two time-dependent potential barriers for polaritons. Polaritons sliding down to the potential well reform new quantum state. The time-integrated PL images at three distinct separations of the two laser beams are shown in figures 2(a)–(c). As the two laser beams leaving further apart, the number of nodes of the highest constrained quantum states is increased. By tuning the separation with sub-micron precision, we can obtain the uppermost quantum state of the harmonic oscillator with n_SHO = 3, 4, and 5, corresponding to beam separations at 4.0, 4.5, and 5.3 μm, respectively. The energy spacing between the adjacent quantum states does decrease with the trap width increasing (energy level spacing is 6.2 meV, 4.5 meV and 4.0 meV). This phenomenon has been demonstrated in early work [20]. Here we reveal the underlying dynamics which was absent in former investigations. In the time-resolved angular distributions, the process of combination and redistribution of the polariton wave packets have been clearly observed, as shown in figures 2(d)–(f).

Zoom In Zoom Out Reset image size

In this section, the harmonic/anharmonic oscillator constrained in symmetric/asymmetric potential well can be well manipulated by the light field strengths of the two excitation beams. We record the spatiotemporal oscillator dynamics formed in optically confined polariton condensates. The typical angle-resolved PL images of polaritonic harmonic oscillators are shown in figures 3(a) and (d). When we use two laser beams with the same power to excite the ZnO microwire, symmetric harmonic potential can be formed thus the resulting polariton condensates will be confined within such potential well and follow the dynamics resembling a harmonic oscillator. Here, the strength of each excitation beam is tuned to be slightly beyond the condensation threshold (P_th = 450 nW). The static (top) and transient (middle and bottom) angle-resolved PL images are presented in figure 3(a). In the time-integrated image, the interference pattern for a series of excited constrain states of n_SHO = 10 (node number) to the ground state can be recognized with equal energy spacing (around 2.2 meV), indicating the occupation of quantum harmonic oscillator states. The relative signal strength for the states with different quantum numbers show an energy-dependence. Based on the FARSI technique, the dynamics showing how a quantum harmonic oscillator is formed can be explicitly visualized. Two distinct transient 2D images are shown in figure 3(a) (middle and bottom), presenting pure interference stripes formed by occupying two excited states observed at times of 7.11 ps and 8.31 ps, respectively. The momentum distributions of the instantaneous interference stripes can be well-reproduced using the quantum harmonic oscillator model [19] which are presented by the white dashed curves in figure 3(a). After the ultrafast injection, polaritons prefer to occupy a highly excited state initially and monotonically moves towards lower energies and smaller transverse momenta. In our measurement, we can see that polaritons with n_SHO = 10 transit to the state with n_SHO = 9. Such process will keep on going until the lowest state with n_SHO = 1 is occupied. The polariton wavefunction at the highest confined state has the most significant overlap with the reservoir, therefore exhibit the highest gain [30]. The wave packet only has a small overlap for lower energy states leads to weaker emissions. Indeed, the polaritons can transfer from the top to the bottom of the cascade sequentially passing all the energy levels, this is the progress of bosonic cascade relaxation, where stimulated transitions occur in a ladder of equidistant energy levels [31]. Clearer transitions between more cascading states can be seen in figure 5(a). In addition, the depth of the potential well can be tailored by the optical field strength. If the power density of two laser beams are increased evenly, the depth of the potential well will increase, and the higher excited SHO state featured by larger node numbers will appear.

Zoom In Zoom Out Reset image size

The time-resolved angular distribution of the PL emission in the momentum space is shown in figure 3(b). Initially, polaritons populate preferentially on the uppermost confined energy state with n_SHO = 10. The distribution undergoes a shrinking in the emission angle with a transition from n_SHO = 10 to n_SHO = 9 occurring at t = 8.5 ps (see the black dash line in figure 3(b)). In figure 3(b), it can be distinguished that the nodes marked by 1–10 populated at different emission angles transit to the nodes 1'–9', where the node 4' is formed by combining part of the neighbouring nodes of 4 and 5 of the higher state, and etc. The transition takes place within 2 ps for the two adjacent quantum states. However, at the angle range of >10 degree, the nodes move to a relatively small angle as time going. The general tendency turned to be that the nodes at high state preferentially combine and generate a new one at the low state with small emission angles, while polariton nodes initially formed in larger angles shift towards smaller angles.

The energy redistribution among polaritons after femtosecond pulse excitation leads to a time-dependent red shift in the emission energy, which can be traced in our measurement and is shown in figure 3(c). Here the time-resolved PL images are integrated for all the emission angles at each time instant. A faster red shift can be recognized in the early stage which can be attributed to the stronger interactions among a larger population of polaritons at the beginning of the ejection. Then the redshift is slowed down due to the decreasing of polariton density since polaritons are decayed with lifetimes of a few picoseconds. There is no further supplement after the end of the femtosecond pumping pulse.

By simply tuning the relative intensity of the two excitation beams, an asymmetric optical potential can be formed and the constrained polaritons undergo anharmonic oscillations. The corresponding results for the polariton anharmonic oscillators are shown in figures 3(d)–(f). There is no apparent difference in the time-integrated and time-resolved 2D distributions of the PL emissions (shown in figure 3(d)) compared to those obtained for the polariton harmonic oscillators. The dynamical process presented in figure 3(e) follows a different scenario compared to that shown in figure 3(b). The signal first appears on the right side where stronger excitation takes place, while the interference stripes appear later at about 8 ps. Generally, a high contrast of the interference stripes requires comparable population of the two coherent polariton wave packets. Based on this, the observed contrast of the interference pattern can be used to indicate the relative intensity of the polariton wave packets created by two pumping pulses. In the asymmetric excitation case, the polariton populations need a few picoseconds to reach an equivalent level on the two sides, the corresponding dynamics are shown in figures 3(e) and (f). In figure 3(f), the red shift exhibits an extra slow region at the beginning from about 4.5 ps to 9.1 ps (lasting for about 4.6 ps), which can be attributed to that stronger excitation leading to a big polaritonic population, resulting in intense interaction between polaritons which accelerate the process of condensation. Therefore, the polariton condensate first appears in the area of strong excitation. In this case, femtosecond-resolved dynamics in both energy and angle degrees of freedom can be revealed for the polariton harmonic oscillator in a confined potential well at room temperature. The transient potential landscapes and the dynamics can be precisely tailored by the external optical field, which provides a unique platform for the manipulation of cavity polariton dynamics.

In this section, symmetric transient potential wells are realized by tuning the relative delay time of the two exciton pulses, which is realized through a precisely controlled delay line. The anharmonic oscillator dynamics has been realized in these asymmetric potential wells caused by the time delay. Here, it should be noted that the power of the two beams is slightly lower than the condensate threshold. In this case, condensation cannot occur for a single beam excitation. Only when the two laser beams come together can polaritons be sufficiently excited in the ZnO WG microcavity to form new quantum states. The dynamics of the polaritons are driven in the temporally tailored potential wells.

When the femtosecond laser pulse illuminates the ZnO microwire, the exciton reservoir will be generated which performs as a time-dependent potential barrier. Dynamically, part of reservoir excitons couple with cavity photons to produce polaritons. Another exciton reservoir is excited by the second beam which is delayed by a few picoseconds with respect to the first coming beam. The two laser beams can form a time-dependent potential well. The polaritons trapped in the potential well undergo coherent manipulations and quantum harmonic oscillator states can be formed. In our experiment, we observe the dynamics of the interference patterns of polariton condensates constrained in temporally manipulated potential wells.

As shown in figure 4, two laser beams with equal power are focused on the ZnO microwire at a spatial separation of about 5.1 μm to excite polaritons. The second laser pulse illuminating the sample on the right-hand side comes at the delays of 0 ps, 3 ps, 6 ps and 9 ps, respectively. The resulting static angular distributions of the PL emissions are shown in figures 4(a)–(d). As the time delay gets bigger, the signals on the right side become stronger compared to those on the left side, which are clearly shown by the integrated signal of the highest excited state at the bottom of the figures (white lines). Each femtosecond excitation ignites a dynamical exciton reservoir. When the two laser pulses come at different instances, a transient potential well can be produced which undergo distinct development, as illustrated in the inserted figures in figures 4(a)–(d).

Zoom In Zoom Out Reset image size

Varying the time delay can produce transient asymmetric potential wells, therefore resulting in polariton anharmonic oscillators. These can be clearly visualized in the time-resolved angular distributions of the PL emission shown in figures 5(a)–(e). In these figures, we can see that the asymmetry of the signal strength on the right side with respect to that on the left side is getting bigger as the delay becomes larger. In addition, when we increase the time delay between the two pumping pulses, the dynamics of the overall polariton yields can be manipulated, the distribution of polariton population can be illustrated by projecting the signals in figures 5(a)–(e) onto the time axis, which is shown in figure 5(f). We found that the maximum population will shift with the time delay. In this set of experiments, the first beam cannot create significant polariton condensates without the participation of the second beam. Only after the second beam arrives at a certain delay, the transient potential barrier created by two beams makes the polaritons being constrained and occupying the harmonic oscillator states. The whole dynamical behavior of the constrained polaritons is determined by the instantaneous potential landscapes formed by the two delayed laser pulses.

Zoom In Zoom Out Reset image size

The dynamics of the polariton harmonic/anharmonic oscillator are simulated using the Gross–Pitaevskii equation [32–34]. Due to the ultrafast injection, the potential barrier caused by the optical field disappears in hundreds of femtoseconds. The potential formed by the induced exciton reservoir possesses a longer lifetime thus dominates the polariton harmonic oscillator formation and relaxation. In addition, hot excitons created by nonresonant excitation and reservoir excitons relaxed from hot excitons contribute to the generation of potential wells.

The equations are written as follows.

$$\begin{equation}\frac{\partial {n}_{\mathrm{p}}}{\partial t}=P(x,t)-{\gamma }_{\mathrm{p}}{n}_{\mathrm{p}}-r{n}_{\mathrm{p}}{n}_{\mathrm{R}}\end{equation} \tag{ 1 }$$

$$\begin{equation}\frac{\partial {n}_{\mathrm{R}}}{\partial t}=r{n}_{\mathrm{p}}{n}_{\mathrm{R}}-R{n}_{\mathrm{R}}{\left\vert \psi \right\vert }^{2}-{\gamma }_{\mathrm{R}}{n}_{\mathrm{R}}\end{equation} \tag{ 2 }$$

$$\begin{align}i\frac{\partial \psi }{\partial t}& =\left[-\frac{\hslash }{2{m}^{{\ast}}}{\nabla }^{2}+{g}_{\mathrm{R}}{n}_{\mathrm{R}}+{g}_{\mathrm{p}}{n}_{\mathrm{p}}+{g}_{\mathrm{c}}{\left\vert \psi \right\vert }^{2}\right]\psi \\ & \quad +i(R{n}_{\mathrm{R}}-{\gamma }_{\mathrm{c}})\psi .\end{align} \tag{ 3 }$$

Here P(x, t) is the pump power. ψ represents polariton wavefunction. n_p(n_R) and γ_p(γ_R) represent the density and the decay rate of the hot excitons (reservoir excitons), respectively. r represents the energy relaxation rate of the hot excitons into the reservoir excitons. g_p, g_R and g_c represent the contact interaction strength. m* is the effective mass of polariton. R stands for the scattering rate from the exciton reservoir to the lower polariton branch. The simulated result showing polariton harmonic oscillator state transiting from three nodes to two and eventually towards one node is presented in figure 6. The strength of the signal gradually decays as time going. These phenomena agree qualitatively with the experimental observations for polariton harmonic oscillators shown in figures 2 and 3.

Zoom In Zoom Out Reset image size