Coherent versus incoherent excitation dynamics in dissipative many-body Rydberg systems

We study the impact of dephasing on the excitation dynamics of a cloud of ultracold two-level Rydberg atoms for both resonant and off-resonant laser excitation, using the wave-function Monte Carlo technique. We find that while for resonant laser driving, dephasing mainly leads to an increase of the Rydberg population and a decrease of the Mandel $Q$ parameter, at off-resonant driving strong dephasing toggles between direct excitation of pairs of atoms and subsequent excitation of single atoms, respectively. These two excitation mechanisms can be directly quantified via the pair-correlation function, which shows strong suppression of the two-photon resonance peak for strong dephasing. Consequently, qualitatively different dynamics arise in the excitation statistics for weak and strong dephasing in off-resonant excitation. Our findings show that time-resolved excitation number measurements can serve as a powerful tool to identify the dominating process in the system's excitation dynamics.

Figure 1

$\left(\mathrm{a}\right)$ Mean Rydberg population $\langle \mathcal{N}\rangle$ as a function of time and $\left(\mathrm{b}\right)$ pair-correlation function for different dephasings, $\Gamma =0$ (blue, solid), $\Gamma /2\pi =0.1$ MHz (red, dashed), and $\Gamma /2\pi =2$ MHz (green, dash-dotted). The inset in (a) shows the Mandel $Q$ parameter as a function of time. The pair-correlation function is evaluated at $t=10\mu \mathrm{s}$. Further parameters: $N=40$, $C_6/2\pi =16\mathrm{GHz}\mu {\mathrm{m}}^6$, $\Omega /2\pi =0.8$ MHz, $\gamma =0.025$ MHz, $\Delta =0$, and one-dimensional trap of length $L_1\mathrm{D}=15\mu \mathrm{m}$.

Figure 2

$\left(\mathrm{a}\right)$ Mean Rydberg population $\langle \mathcal{N}\rangle$ and $\left(\mathrm{b}\right)$ Mandel $Q$ parameter as a function of the dephasing. The different symbols indicate different evaluation times, $t=\{1,2,5,10\}\mu \mathrm{s}$, corresponding to the data points marked by circles, diamonds, squares, and triangles, respectively. Further parameters as in Fig. 1.

Figure 3

Excitation probability $P_m$ for two different dephasings, $\Gamma =0$ (blue, left panel) and $\Gamma /2\pi =3$ MHz (red, right panel), at three different times. Further parameters as in Fig. 1.

Figure 4

Sketch of the dominant off-resonant excitation mechanisms in an illustrative few-excitations sample. The blue bent lines indicate coherent excitation; the red straight lines indicate incoherent excitation. The thickness of the arrows quantifies the strength of the coupling. The gray boxes indicate the possible energies of the respective states in the rotating frame of Eq. (1) up to a certain energy cutoff.

Figure 5

$\left(\mathrm{a}\right)$ Mean Rydberg population $\langle \mathcal{N}\rangle$ and $\left(\mathrm{b}\right)$ Mandel $Q$ parameter as a function of time for different dephasings, $\Gamma /2\pi =0.05$ MHz (blue, solid) and $\Gamma /2\pi =4$ MHz (red, dashed). The insets show enlarged details of the respective short-term dynamics. Further parameters: $N=50$, $C_6/2\pi =16\mathrm{GHz}\mu {\mathrm{m}}^6$, $\Omega /2\pi =1$ MHz, $\gamma =0.025$ MHz, $\Delta /2\pi =10$ MHz, and cylindrical trap with radius $R=1.65\mu \mathrm{m}$ and length $L=6\mu \mathrm{m}$.

Figure 6

Pair-correlation function as a function of time for different dephasings, $\left(\mathrm{a}\right)$ $\Gamma /2\pi =0.05$ MHz and $\left(\mathrm{b}\right)$ $\Gamma /2\pi =4$ MHz. Further parameters as in Fig. 5. In (a), Rabi oscillations can be seen in the pair-correlation function at small times.

Figure 7

Excitation probability $P_m$ for two different dephasings, $\Gamma /2\pi =0.05$ MHz (blue, left panel) and $\Gamma /2\pi =4$ MHz (red, right panel), at four different times. The dashed histograms denote the respective excitation statistics measured with a finite detection efficiency of $\eta =0.8$. Further parameters as in Fig. 5.

Figure 8

$\left(\mathrm{a}\right)$ Difference between quasicoherent ($\Gamma /2\pi =0.05$ MHz) and incoherent ($\Gamma /2\pi =4$ MHz) excitation histograms and $\left(\mathrm{b}\right)$ excitation probability $P_0$ on a logarithmic scale as a function of time. In $\left(\mathrm{b}\right)$, the solid blue curve corresponds to $\Gamma /2\pi =0.05$ MHz, whereas the dashed red one corresponds to $\Gamma /2\pi =4$ MHz. Further parameters as in Fig. 5.

Figure 9

$\left(\mathrm{a}\right)$ Mean Rydberg population $\langle \mathcal{N}\rangle$ as a function of time and $\left(\mathrm{b}\right)$ pair-correlation function, comparing MCWF model (blue, solid) and rate equation model (red, dashed) for different dephasings. The pair-correlation function is evaluated at $t=10\mu \mathrm{s}$. To improve visibility, only the lowest-order peaks of the pair-correlation function are shown. Further parameters: $N=30$, $C_6/2\pi =16\mathrm{GHz}\mu {\mathrm{m}}^6$, $\Omega /2\pi =0.8$ MHz, $\gamma /2\pi =0.125$ MHz, $\Delta /2\pi =12$ MHz, and one-dimensional trap of length $L_1\mathrm{D}=16.2\mu \mathrm{m}$.

Figure 10

Excitation probability $P_m$ at different times for the experimental trap geometry of Ref. [6], $\Delta /2\pi =15$ MHz and a density of $1.5\times {10}^{12}$ cm${}^{-3}$, obtained using rate equation calculations [6, 27].