We demonstrate a non-equilibrium phase transition in a dilute thermal atomic gas. The phase transition, between states of low and high Rydberg occupancy, is induced by resonant dipole-dipole interactions between Rydberg atoms. The gas can be considered as dilute as the atoms are separated by distances much greater than the wavelength of the optical transitions used to excite them. In the frequency domain we observe a mean-field shift of the Rydberg state which results in intrinsic optical bistability above a critical Rydberg number density. In the time domain we observe critical slowing down where the recovery time to system perturbations diverges with critical exponent α = −0.53 ± 0.10. The atomic emission spectrum of the phase with high Rydberg occupancy provides evidence for a superradiant cascade.Non-equilibrium systems displaying phase transitions are found throughout nature and society, for example in ecosystems, financial markets and climate [1]. The steady state of a non-equilibrium system is a dynamical equilibrium between driving and dissipative processes. In atomic physics, one of the most studied non-equilibrium phase transitions is optical bistability where the driving is provided by a resonant laser field and the dissipation is inherent in the atom-light interaction. In most examples of optical bistability feedback is provided by an optical cavity, as in the pioneering work of Gibbs [2,3]. However, bistability can also arise in systems where many dipoles are located within a volume which is much smaller than the optical wavelength; in this case the feedback is due to resonant dipole-dipole interactions [4,5]. This latter case is known as intrinsic optical bistability [6] and has, so far, only been observed in an up-conversion process between densely packed Yb 3+ ions in a solid-state crystal host cooled to cryogenic temperatures [7]. Intrinsic optical bistability generally cannot be observed for simple two-level systems such as atomic gases, because the resonance broadening, which is larger than the line shift [8], suppresses the bistable response [9,10].A solution to this problem is provided by highlyexcited Rydberg states, where the dipole-dipole induced level shifts between neighbouring states can be much larger than the excitation linewidth. This property of optical excitation of Rydberg atoms, known as dipole blockade [11], enables a diverse range of applications in quantum many-body physics, quantum information processing [12], non-linear optics [13] and quantum optics [14][15][16][17]. An interesting feature of Rydberg systems is that the range of the interaction can be much larger than the optical excitation wavelength, giving rise to non-local interactions [18]. This also creates the possibility of observing intrinsic optical bistability, and hence non-equilibrium phase transitions [19] over macroscopic, optically-resolvable length scales.In this letter, we demonstrate a non-equilibrium phase transition in a thermal Rydberg ensemble. In contrast to previous experiments, we directly observe...

Terahertz (THz) near-field imaging is a flourishing discipline [1, 2], with applications from fundamental studies of beam propagation [3] to the characterisation of metamaterials [4,5] and waveguides [6,7]. Beating the diffraction limit typically involves rastering structures or detectors with length scale shorter than the radiation wavelength; in the THz domain this has been achieved using a number of techniques including scattering tips [8,9] and apertures [10]. Alternatively, mapping THz fields onto an optical wavelength and imaging the visible light removes the requirement for scanning a local probe, speeding up image collection times [11,12]. Here we report THz to optical conversion using a gas of highly excited 'Rydberg' atoms. By collecting THz-induced optical fluorescence we demonstrate a real-time image of a THz standing wave and we use well-known atomic properties to calibrate the THz field strength.Atoms make excellent electromagnetic field sensors because narrow line-width atomic transitions couple strongly to EM fields, giving atoms a sensitive, narrowband response. In addition, each atom of the same isotope is identical and has well studied, permanent properties which facilitate easy calibration to SI units. Atomic states that couple to multiple transitions offer an interface between different frequency regimes. In this way atomic ground states have been used to map microwave fields onto an optical probe [13]. However atomic ground states are only sensitive to a limited selection of microwave frequencies. In contrast, highlyexcited Rydberg atoms couple to strong, electric dipole transitions across a wide range of microwave and THz frequencies, making them ideal candidates for field measurement and for frequency standards in the millimeter wave and THz range [14]. Previous methods for THz imaging with Rydberg atoms used the THz radiation to ionise the atoms [15,16]. More recently optical read-out of Rydberg states was demonstrated in a room-temperature alkali-metal vapour using electromagnetically induced transparency (EIT) [17]. The 'Rydberg EIT' technique has since been exploited to readout radio frequency fields [18], to demonstrate precision microwave electrometry [19][20][21] and for sub-wavelength imaging of microwave fields [22]. * c.g.wade@durham.ac.ukIn distinction to the EIT technique we make direct use of THz-induced optical fluorescence to demonstrate THz imaging. An overview of our THz imaging setup is shown in Figure 1a. Infrared laser beams forming a three-step ladder excitation scheme [23] are co-axially aligned with a continuous wave (CW) THz beam and pass through a caesium vapour in a 2 mm long quartz cell. In regions where both the THz field and the laser beams are present, atoms are excited to a Rydberg state and subsequently decay with fluorescence at visible wavelengths. The fluorescence is imaged by a consumer digital camera, and a typical 0.5 s exposure is shown in Figure 1b. In Figure 1c we show THz transition frequencies and calculated reduced dipole matrix elements,d, for...

We investigate the nonequilibrium dynamics of a driven-dissipative spin ensemble with competing power-law interactions. We demonstrate that dynamical phase transitions as well as bistabilities can emerge for asymptotic van derWaals interactions, but critically rely on the presence of a slower decaying potential core. Upon introducing random particle motion, we show that a finite gas temperature can drive a phase transition with regards to the spin degree of freedom and eventually leads to mean-field behavior in the high-temperature limit. Our work reconciles contrasting observations of recent experiments with Rydberg atoms in the cold-gas and hot-vapor domain, and introduces an efficient theoretical framework in the latter regime

We observe and characterize intrinsic optical bistability in a dilute Rydberg vapor. The bistability is characterized by sharp jumps between states of low and high Rydberg occupancy with jump up and down positions displaying hysteresis depending on the direction in which the control parameter is changed. We find that the shift in frequency of the jump point scales with the fourth power of the principal quantum number. Also, the width of the hysteresis window increases with increasing principal quantum number, before reaching a peak and then closing again. The experimental results are consistent with predictions from a simple theoretical model based on semiclassical Maxwell-Bloch equations including the effects of broadening and frequency shifts. These results provide insight to the dynamics of driven dissipative systems.

There are few demonstrated examples of phase transitions that may be driven directly by terahertz frequency electric fields, and those that are known require field strengths exceeding 1 MV cm−1. Here we report a non-equilibrium phase transition driven by a weak (≪1 V cm−1), continuous-wave terahertz electric field. The system consists of room temperature caesium vapour under continuous optical excitation to a high-lying Rydberg state, which is resonantly coupled to a nearby level by the terahertz electric field. We use a simple model to understand the underlying physical behaviour, and we demonstrate two protocols to exploit the phase transition as a narrowband terahertz detector: the first with a fast (20 μs) non-linear response to nano-Watts of incident radiation, and the second with a linearised response and effective noise equivalent power ≤1 pW Hz−1/2. The work opens the door to a class of terahertz devices controlled with low-field intensities and operating in a room temperature environment.