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arXiv:2001.04999 · Physical Review Research

Non-Markovian super-superradiance in a linear chain of up to 100 qubits

Fatih Dinç, Agata M. Brańczyk

Published Dec 19, 2019• 44 citations
arXivHTMLPDF

Abstract

This paper shows how super-superradiance in a waveguide scales with the number of atoms. Usually, superradiance occurs when atoms are separated by distances much smaller than their transition wavelengths, but in waveguide structures, this collective emission phenomenon can persists for even larger periodic separation. Moreover, in a waveguide, this collective decay can become even more superradiant, i.e., super-superradiant. Here, the authors prove that super-superradiance scales linearly with the qubit number, analogous to Dicke superradiance, but with a larger prefactor.

DOI
10.1103/physrevresearch.1.032042

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This paper shows how super-superradiance in a waveguide scales with the number of atoms. Usually, superradiance occurs when atoms are separated by distances much smaller than their transition wavelengths, but in waveguide structures, this collective emission phenomenon can persists for even larger periodic separation. Moreover, in a waveguide, this collective decay can become even more superradiant, i.e., super-superradiant. Here, the authors prove that super-superradiance scales linearly with the qubit number, analogous to Dicke superradiance, but with a larger prefactor.
Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength λλλ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than λλλ. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
We study the collective decay rates of multidimensional quantum networks in which one-dimensional waveguides form an intersecting hyperrectangular lattice, with qubits located at the lattice points.We introduce and motivate the dimensional reduction of poles (DRoP) conjecture, which identifies all collective decay rates of such networks via a connection to waveguides with a one-dimensional topology (e.g., a linear chain of qubits).Using DRoP, we consider many-body effects such as superradiance, subradiance, and bound states in continuum in multidimensional quantum networks.We find that, unlike one-dimensional linear chains, multidimensional quantum networks have superradiance in distinct levels, which we call multidimensional superradiance.Furthermore, we generalize the N -3 scaling of subradiance in a linear chain to d-dimensional networks.
Fully excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954 [Phys. Rev. 93, 99 (1954)]. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength $\ensuremath{\lambda}$ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of distant noninteracting atoms with mutual separations much larger than $\ensuremath{\lambda}$. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
In quantum optics, superradiance is a phenomenon in which a system of NNN fully excited quantum emitters radiate intense flashes of light during collective decay. However, computing its peak intensity exactly for many spatially separated emitters remains challenging due to the exponential growth of the underlying Hilbert space with system size NNN. Based on third-order cumulant expansion methods, we present general scaling laws for the expononent of the peak emission rate as a function of the emitter number in free-space emitter arrays and arrays coupled to one-dimensional waveguide reservoirs. We find, that for 1D chains in free-space the peak emission rate scales linearly with NNN, while for 2D and 3D arrays with finite emitter spacing it scales superlinearly but sub-quadratically. For emitter chains coupled to waveguide reservoirs we find that the peak emission rate scales quadratically with NNN.
Recently, it has been suggested that the collective radiative decay of two point-like quantum emitters coupled to a waveguide, separated by a distance comparable to the coherence length of a spontaneously emitted photon, leads to an apparent "superradiance paradox" by which one cannot decide whether independent or collective emission occurs. Here we suggest an integrated optics platform to emulate the superradiance paradox, based on photon escape dynamics in waveguide lattices. Remarkably, Markovian decay dynamics and independent photon emission can be restored by frequent (Zeno-like) observation of the system.
A recent experiment reveals the linear scaling property of the superradiant emission rate for a trapped atom cloud that is excited by weak and short light pulses. We adopt a real-space approach to numerically demonstrate that such a linear scaling law can be interpreted as single-photon superradiance, in both the time domain and the frequency domain. The dependence of the single-photon superradiant emission rate on the distance between atoms is investigated. We further study the single-photon superradiance for artificial atoms that have deviations in transition frequencies and decay rates.