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arXiv:1909.00999 · Physical Review Research

Spontaneous formation of a macroscopically extended coherent state

C. Braggio, F. Chiossi, G. Carugno, A. Ortolan, G. Ruoso

Published Jul 13, 2020• 15 citations
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Abstract

The authors show superfluorescent emission by a large ensemble of ions ($\ensuremath{\sim}$\,10^12) embedded in a rare earth doped crystal. The paper shows how the spontaneous formation of a single macroscopic dipole takes place, triggered by excited ions coherently interacting via a common light field and initiated by the vacuum fluctuations.

DOI
10.1103/physrevresearch.2.033059

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The authors show superfluorescent emission by a large ensemble of ions (\ensuremath∼\ensuremath{\sim}\ensuremath∼,10^12) embedded in a rare earth doped crystal. The paper shows how the spontaneous formation of a single macroscopic dipole takes place, triggered by excited ions coherently interacting via a common light field and initiated by the vacuum fluctuations.
Superfluorescence (SF) is the emission from a dense coherent system in population inversion formed from an initially incoherent ensemble. This is characterized by an induction time (${\ensuremath{\tau}}_{\mathrm{D}}$) for the spontaneous development of the macroscopic quantum coherence. Here we report detailed observation of SF on an ultrafast timescale from a quantum ensemble of coherent excitons in highly excited intrinsic-bulk ZnTe single crystal at 5 K, showing a characteristic ${\ensuremath{\tau}}_{\mathrm{D}}$ from 40 ps to 10 ps, quantum noise and fluctuations, and quantum beating and ringing. From this clear observation of SF from a spontaneous coherence of excitons bound to impurities and defect states, we infer that this is indicative of the formation of a spontaneous Bose-Einstein condensation (BEC) of excitons on an ultrafast timescale. The population density and dephasing time (T2{T}_{2}T2​ or T2∗{T}_{2}^{*}T2∗​) of exciton are two controlling factors in the generation of SF from the BEC.
Spontaneous decay is a phenomenon that has been described for the first time by Dirac, Wigner and Weisskopf, at the early ages of the development of quantum electrodynamics. The theory is applicable to a multi-body system only when atoms don’t interact during their decay. Dicke introduces in his seminal paper the case where this assumption doesn’t hold. The results he obtains not only tell that the system emits pulses, but the pulse duration now depends on 1/N, where N is the number of participating atoms to the process. The pulses temporal profile is described by a squared hyperbolic secant function. The resulting emission intensity scales as N^2. The atomic system radiates more intensively than the ordinary fluorescent emission, this is the reason why the process is called superradiance, or by a generalization to extended systems, superfluorescence. The superradiant emission has preferential escape directions, depending on the atomic sample shape. Superradiance is a collective process and it takes place when the group of excited atoms is left unper- turbed during the formation of of the macroscopic dipole. A fundamental difference compared to the spontaneous and stimulated emission processes is that all atoms act together as a single entity and it isn’t possible to identify single atoms involved. This remarkable behaviour is manifest when the atomic coherence of the system, while influenced by environmental interactions that cause dephasing in atoms, persists for a sufficient interval of time. Typical dephasing mechanisms, such as collisions in gases or lattice phonon interactions in crystals, make its experimental observation difficult. A possible solution to this problem is the use of optical crystals doped with rare-earths that are characterized by long and narrow levels lifetimes.
This thesis work contributes to the effort of detecting single rare earth ions doped into crystals, an operation crucial for the development of rare earth quantum computer hardware. Doping crystals with rare earth elements, their trivalent ions substitute some of the crystal’s original bonds. These ions have a partially filled 4f shell, protected by the full 5s and 5p shell from the environment which makes them good candidates for qubits. Because not every ion experiences the same electric field from the imperfect crystal, their total linewidth is inhomogeneously broadened. If the doping is sufficiently low and the crystal sufficiently small, each ion undergoes a different optical shift and can thus be addressed separately. Communication between ions happens due to their permanent dipole moments which change according to their energy level. So far no single ions could be detected in Lund because highly doped bulk crystals were used. It was nevertheless tried to construct quantum logic gates using qubits that consisted of an ensemble of ions. Constructing logic gates with these means that every single ion of one qubit needs to be able to communicate with every single ion of another qubit, a method that becomes increasingly difficult when more and more qubits are to be entangled. Connecting as many qubits as possible is a crucial step in building a quantum computer that could outperform classical computers and this could be facilitated if every qubit consisted of only one ion which is the reason for the recent explorations towards nano crystals. This development also makes it possible to address another problem of rare earth ions, their low probability of spontaneous emission. Placing nano crystals into an optical cavity promises the enhancement of spontaneous emission by the Purcell effect. Ideal cavities are Fiber Fabry-Pérot resonators of which one side consists of a mirror coated fiber tip and the other of a plane mirror functioning as the substrate for the nano crystals. It was the aim of this thesis to build a cryostat holder that would bring these two mirrors together with high stability and would allow for vertical and horizontal scanning.
When a quantum system is put into an excited state, it will decay back to the ground state through a process termed spontaneous emission.It is generally assumed that spontaneous emissions between different individual emitters will not be coherent with each other; to produce coherent light, one would need population inversion and stimulated emission.In this work, we show that an optically thin ensemble of 11 000 radiating atoms spontaneously organizes to produce spatially coherent light.The reason for this coherence is collective coupling of the individual emitters via Dicke superradiance and subradiance (as opposed to amplification through stimulated emission).