• Rydberg atom
• Laser cooling and trapping
• Absorbing-state phase transition

Absorbing-state phase transitions are non-equilibrium phase transitions that can occur, for instance, in models describing the growth of bacterial colonies or the spreading of an infectious disease among a population. Despite the fact that this class of non-equilibrium critical phenomena has been investigated for several decades [1], it has been challenging to find experimental systems that unambiguously manifest it.
The simplest system in which absorbing-state phase transitions occur is made of identical components, arranged in a lattice with fixed site distances, with two different internal states: an excited state, which is energetically unstable, and a ground state, which is stable. The particles of the system can change their state via two stochastic processes: the decay, a one-way process consisting in the particle going from the excited to the ground state, and the offspring reproduction, a two-way process where one particle is excited (or de-excited) only if there is a pre-existent excitation next to it. The particular nature of the excitation process implies that the ground state represents the absorbing-state of the system, a configuration that can be reached by the dynamics but cannot be left (like a sticky wall in a random walk process).
The same particular nature of the excitation imposes to choose an initial state with at least one excitation to study the phase transition. The phase transition is observed varying the relative probability of the two processes. If decay dominates, the system will go towards the absorbing state. If offspring reproduction prevails, the system will reach a stationary state where there is a fixed number of excitations in the system that is dependent on the value of the ratio between the excitation and decay rates. With the two states established above, the system becomes critical at the transition point, where it exhibits long range correlation and is characterized by its scaling behaviours, specifically, the scaling exponents.
To observe an absorbing-state phase transition using a gas of cold 87Rb atoms, we need to replicate the peculiar nature of the excitation process. In our case, we satisfy these conditions using a Rydberg level as the excited state. Rydberg atoms have one or more electrons excited to high principal quantum number, showing exaggerated properties. They have long lifetimes, of the order 100 µs (for the state 70S that we have employed) and interact strongly with each other due to of their large van der Waals interactions. This interaction energy, of the form C6/R^6, is responsible for the so-called dipole blockade, in which the creation of more than one Rydberg excitation within a certain radius is strongly suppressed (in our experiment the blockade radius is ~10 µm). However, if the excitation laser is off resonance with detuning Delta for an isolated atom, it is resonant for an atom that is in a shell of distance called facilitation radius R_fac=((C6*2*pi)/(h*Delta))^(1/6) from a Rydberg atom. This off-resonant excitation is called facilitation and is caused by the repulsive nature of the van der Waals interactions between Rydberg atoms in S state. The other process that has to be present in the system, the decay, is simply realized by the spontaneuos decay from the Rydberg level to the ground state of the atom. In addition to these processes, necessary to observe the absorbing-state phase transition, there is a third one: the atoms in the gas can be excited also in the absence of a nearby Rydberg atom. This spontaneous excitation is less likely to happen when the excitation laser is out of resonance but, especially for high values of the Rabi frequency of the excitation transition, the probability is not neglible. This extra process is responsible for the smoothing of the phase transition in our measurements.
In our experimental apparatus, a 87Rb atomic gas is cooled at T = 150 µK and confined within a 3D Magneto Optical Trap (MOT). After being trapped, the atoms are excited to the Rydberg state 70S by a two-step excitation process. The excitation lasers (responsible for the offspring reproduction) shine the atoms for a time much longer than the Rydberg lifetime. In this way we implement an open driven many-body quantum system, in which we observe a change of the global state of the system from the absorbing state to the blockaded state, varying the power of the excitation laser from 0 to the max. We explored two different geometries for the Rydberg excitation: a quasi-1D geometry, in which the offspring reproduction creates a chain of Rydberg atoms, or a 3D configuration. The main experimental results reported in this thesis are in the quasi-1D configuration, for which Prof. Igor Lesanovsky and co-workers at the University of Nottingham developed a mean-field model and numerical simulations, taking into account also position disorder and atomic motion, two important features of the real system of cold Rydberg atoms we have experimentally studied.
[1] Haye Hinrichsen. Non-equilibrium critical phenomena and phase transition into absorbing states. Advances in Physics, 49(7):815-958, 2000.