Studies of subradiance in a chain N two-level atoms in the single excitation regime focused mainly on the complex spectrum of the effective Hamiltonian, identifying subradiant eigenvalues. This can be achieved by finding the eigenvalues N of the Hamiltonian or by evaluating the expectation value of the Hamiltonian on a generalized Dicke state, depending on a continuous variable k. This has the advantage that the sum above N can be calculated exactly, such that N becomes a simple parameter of the system and no more the size of the Hilbert space. However, the question remains how subradiance emerges from atoms initially excited or driven by a laser. Here we study the dynamics of the system, solving the coupled-dipole equations for N atoms and evaluating the probability to be in a generalized Dicke state at a given time. Once the subradiant regions has been identified, it is simple to see if subradiance is being generated. We discuss different initial excitation conditions that lead to subradiance and the case of atoms excited by switching on and off a weak laser. This may be relevant for future experiments aimed at detecting subradiance in ordered systems.
Studies of subradiance in a chain N two-level atoms in the single excitation regime focused mainly on the complex spectrum of the effective Hamiltonian, identifying subradiant eigenvalues. This can be achieved by finding the eigenvalues N of the Hamiltonian or by evaluating the expectation value of the Hamiltonian on a generalized Dicke state, depending on a continuous variable k. This has the advantage that the sum above N can be calculated exactly, such that N becomes a simple parameter of the system and no more the size of the Hilbert space. However, the question remains how subradiance emerges from atoms initially excited or driven by a laser. Here we study the dynamics of the system, solving the coupled-dipole equations for N atoms and evaluating the probability to be in a generalized Dicke state at a given time. Once the subradiant regions has been identified, it is simple to see if subradiance is being generated. We discuss different initial excitation conditions that lead to subradiance and the case of atoms excited by switching on and off a weak laser. This may be relevant for future experiments aimed at detecting subradiance in ordered systems.
We study the collective spontaneous emission of a linear atomic chain excited by a single photon. The interaction between the atoms and the common vacuum field can significantly change the eigenenergy and the spontaneous emission rate of the system. Due to the dipole-dipole interactions, the system prepared in a single-photon timed Dicke state is the superposition of superradiant and subradiant eigenstates that can have a nonexponential decay dynamics. We can tune the frequency and linewidth of the superradiant and subradiant emission from a timed Dicke state by changing the direction of the atomic dipole moment or the atomic separation. In addition, the emission direction of the superradiant and subradiant photons also depends on the polarization of the atoms.
We explore the formation of Dicke states. A system consisting of two two-level atoms located in the right Rindler wedge, has investigated to determine the conditions under which the superradiant or subradiant state can be formed. The dynamics of N two-level atoms forming symmetric state has also been analyzed and showed that the probability to excite any one atom of a collection of N atoms is related to the probability of exciting a single atom. We derive the analytical expression for the joint excitation probability which demonstrates the the interference effect. These findings provide new insights into the behavior of quantum systems in non-inertial frames and contribute to the broader understanding of relativistic quantum information theory.
We report a time-resolved study of collective emission in dense ensembles of two-level atoms. We compare, on the same sample, the buildup of superradiance and subradiance from the ensemble when driven by a strong laser. This allows us to measure the dynamics of the population of superradiant and subradiant states as a function of time. In particular, we demonstrate the buildup in time of subradiant states through superradiant dynamics. This illustrates the dynamics of the many-body density matrix of superradiant ensembles of two-level atoms when departing from the ideal conditions of Dicke superradiance, in which symmetry forbids the population of subradiant states.
We investigate collective behaviour that appears in open, many-body systems of two- and four-level atoms. Here, ``open" refers to the system interacting with an external environment that causes dissipation. We derive a general open quantum master equation to describe the system dynamics only, independent of this environment. We identify processes such as coherent exchange of virtual photons and modified decay rates caused by long-range interactions between all pairs of atoms that scale with distance by inverse power laws. We explore excitation transport within a one-dimensional chain of atoms where the atomic transition dipoles are coupled to the free radiation field. When the interatomic spacing is smaller than or comparable to the wavelength of light associated with the photon emitted from a given transition, virtual photon exchange interactions facilitate excitation transport through the chain. Atomic systems coupled to an environment display dissipative dynamics, however subradiant transport is exhibited from a variety of initial states; spontaneous emission from the chain occurs at a rate much slower than that for an individual atom. In particular, we find a region within the decay spectrum that consists entirely of subradiant states with a corresponding linear dispersion relation in the interaction energy. Identifying this subspace allows for the dispersionless transport of wave packets over long distances with near-zero decay. Moreover, the group velocity of the wave packet and direction of the transport can be controlled via an external uniform magnetic field while preserving its subradiant character. We discuss a number of experimental considerations to justify the feasibility and robustness of this protocol. Initial state preparation is outlined, utilising external laser driving to excite the system into the single excitation sector. Furthermore, we consider positional disorder by explicitly accounting for the external atomic degrees of freedom -- position and momentum -- which allows us to model the positions of all atoms by a motional state representing the occupation of a lattice well with a given width. These discussions are made in the low-temperature limit, where the atomic motion is essentially frozen, and we identify that subradiant transport is indeed robust. Finally, we explore the experimental limits of interatomic spacing and imperfect filling within an experimentally achievable optical lattice. We calculate the photon emission rate -- an experimentally measurable quantity -- and compare the emission spectra to our analysis. By limiting parameters to those achieved experimentally, we observe a reduction, yet not an absence, of collective behaviour. The simplicity and versatility of this system, together with the robustness of subradiance against disorder, makes it relevant for a range of applications such as lossless energy transport and long-time light storage. The lifetime of an atomic excitation could be increased by a factor of thousands to millions for a chain of atoms under the conditions that we explore in this thesis.
Since Dicke's seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes. Here, we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model.
The cause of decoherence in a quantum system can be traced back to the interaction with the environment. As it has been pointed out by Dicke, in a system of N two-level atoms, where each of the atoms is individually dipole coupled to the environment, there are collective, subradiant states, that have no dipole coupling to photon modes, and therefore, they are expected to decay slower. This property also implies that these type of states decohere slower. We propose a scheme which will create such states. First, the two-level atoms are placed in a strongly detuned cavity and one of the atoms, called the control atom is excited. The time evolution of the coupled atom-cavity system leads to an appropriately entangled state of the atoms. By the aid of a suitable single-atom phase transformation, it is possible to drive the atomic state into the subradiant, i.e., decoherence-free subspace. Up to a certain average number of photons, the result is independent of the state of the cavity. The analysis of the conditions shows that this scheme is feasible with present day techniques achieved in atom-cavity interaction experiments.