Observation of Temperature Effects on False Vacuum Decay in Atomic Quantum Gases

TL;DR

Temperature drives the decay of a false vacuum in an ultracold, coherently coupled two-spin sodium gas. The authors test the finite-temperature extension of instanton theory by measuring the decay time $\tau$ across varied detuning and temperature, showing $\tau$ scales as $\tau = A \frac{e^{\beta E_c}}{\sqrt{\beta E_c}}$ with $\beta=1/(k_B T)$. They find the data collapse when plotting $\tau$ against $\varepsilon_c/(k_B T_{exp})$ and a linear relation $1/(b k_B) \approx 2.02\, T_{exp}$, supporting thermally assisted FV decay. The results validate the Linde extension of FV decay in atomic systems and establish ultracold gases as a platform for exploring out-of-equilibrium field theories and related dissipation effects.

Abstract

Temperature plays a crucial role in metastable phenomena, not only by contributing to determine the state (phase) of a system, but also ruling the decay probability to more stable states. Such a situation is encountered in many different physical systems, ranging from chemical reactions to magnetic structures. The characteristic decay timescale is not always straightforward to estimate since it depends on the microscopic details of the system. A paradigmatic example in quantum field theories is the decay of the false vacuum, manifested via the nucleation of bubbles. In this paper, we measure the temperature dependence of the timescale for the false vacuum decay mechanism in an ultracold atomic quantum spin mixture which exhibits ferromagnetic properties. Our results show that the false vacuum decay rate scales with temperature as predicted by the finite-temperature extension of the instanton theory, and confirm atomic systems as an ideal platform where to study out-of-equilibrium field theories.

Figures (8)

• Figure 1: Relevant temperature scales in the FVD. For temperatures smaller than the one associated with interactions, which in our atomic case are $\hbar|\kappa|n/k_B$ (see later), quantum fluctuations dominate in the FVD process. If the system temperature is higher but still smaller than $E_c/k_B$, the FVD is driven by thermal fluctuations. For higher temperatures, the decay is an incoherent process.
• Figure 2: (a) Potential profiles during the main steps of the protocol. $\textcircled{1}$ Initial preparation in $\ket{\uparrow}$; $\textcircled{2}$ Symmetric configuration for $\delta = 0$; $\textcircled{3}$ Metastable state and absolute ground state at $\delta_f$. $\textcircled{4}$ Potential profile at the critical detuning $\delta_c$. (b),(c) Evolution of the system average magnetization $\langle Z(x)\rangle$ for increasing waiting time $t$. Two different temperature regimes are shown for similar $(\delta_f-\delta_c)/2\pi \sim 60$ Hz, with $T_\text{exp} =$ 1.4(1) $\mu$K (a) and 2.3(1) $\mu$K (b). (d) Survival probability of the FV $F(t)$ in the corresponding two datasets. Error bars represent the standard error of the average magnetization.
• Figure 3: (a) Measured decay time $\tau$ as a function of the parameter $(\delta_f-\delta_c)/|\kappa|n$. The color scale accounts for the different temperatures of each cluster. Each point was obtained from about one hundred experimental realizations. Error bars are given by the experimental uncertainties on $(\delta_f-\delta_c)$ and $|\kappa|n$ and fit uncertainty on $\tau$. The inset shows the seven clusters in which the data are grouped according to the temperature. (b) The lin-log plot of $\tau$ as a function of $\varepsilon_c$ shows a quasi-linear trend with smaller slope for higher temperatures. The temperature for the green and purple datasets are 1.40(3) and 2.26(6) $\mu$K, respectively. Dashed lines are the fits according to Eq. \ref{['eq:tau-fit']}.
• Figure 4: (a) The experimentally measured (diamonds) values of $1/bk_B$ as a function of the atomic temperature $T_\mathrm{exp}$ show a linear dependence. Orange boxes are horizontally bounded by the minimum and maximum temperature in each cluster, while vertical boundaries result from the fit uncertainties on $b$. Points are centered around the mean value of $T_\mathrm{exp}$ for each cluster. The shaded grey area corresponds to the one-$\sigma$ confidence interval of a linear fit. (b) Within the experimental uncertainties, the prefactor $a$ does not show any clear dependence on $T_\mathrm{exp}$ and has a mean value of 0.8(4) ms. (c) The $\tau$ data from Fig. \ref{['fig:fig3']} collapse onto an single curve when plotted as a function of the dimensionless parameter $\varepsilon_c/k_BT_\mathrm{exp}$.
• Figure S1: Experimental sequence. (a) Variation in time of the optical potential $U$. The temperature of the sample can be tuned by varying the trapping potential $U_{\mathrm{evap}}$ at the bottom of the evaporation ramp. The trap is later recompressed in 500 ms to a final radial trapping frequency of 2 kHz. Panel (b) shows that the temperature measured after the recompression ramp varies linearly with the value of $U_{\mathrm{evap}}$. The time sequence of detuning and coupling strength is shown in panel (c) and (d), respectively. For comparison, $|\kappa|n \simeq$ 1 kHz. (e) Phase diagram of the ferromagnetic superfluid mixture showing the paramagnetic (PM), ferromagnetic (FM), and saturated ferromagnetic (S-FM) regions as a function of the detuning and spin interactions in units of the coupling strength. The color code is the same used in Fig. 2 of the main text (blue for $\ket{\uparrow}\xspace$ and red for $\ket{\downarrow}\xspace$). The black line illustrates the path followed by the mixture during the preparation process. The three insets show the potential energy profile in different regions.