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Acronym: SSB-QD-Laser

Project code: PN-III-P4-ID-PCE-2016-0221

Funded by: Romanian National Authority for Scientific Research, UEFISCDI

Contractor: CIFRA-INCDFM

Project director: Dr. Paul Gartner

Start Date: 12 July 2017

End Date: 31 December 2019

Project Summary:

The problem of the onset of lasing as a nonequilibrium phase transition is a debated issue in the case of few- or single-emitter systems, with several nonequivalent lasing criteria being used in the literature. We address this problem by analyzing the spontaneous breaking of the rotation symmetry in the phase space of coherent photonic states. Anomalous averages should appear as a sign of instability to symmetry-spoiling infinitesimal perturbations in the lasing regime, and only there. This way we propose a simple lasing criterion which also identifies the excitation threshold point. The problem will be treated using the P-representation of the photonic density operator, which is defined on the phase space. The accuracy of the simpler, approximate rate equation solution will be checked against the full solution. The result will be generalized to coupled cavity arrays.

A second objective concerns the quantum dot carrier dynamics interacting with a gas of electrons or holes in the spectral continuum provided by either the wetting layer or the barrier bulk states. A similar problem is successfully treated for the carrier-phonon interaction, using the polaronic unitary transform. This goes beyond the usual Born-Markov of the system-reservoir interaction by including quasi-particle renormalization by the same interaction. We treat the problem of a fermionic reservoir on the same footing by identifying the analog unitary transform in the S-matrix of the scattering problem on the quantum dot as scattering center. This procedure will provide accurate calculations of dissipation rates and exciton emission lineshapes as a function of temperature and continuum carrier populations. These are both controllable parameters in a quantum dot device.

Project team:

  1. Paul Gartner - Experienced Researcher
  2. Viorel Dinu - Experienced Researcher
  3. Marian Nita - Experienced Researcher
  4. Valeriu Moldoveanu - Experienced Researcher
  5. Mugurel Tolea - Experienced Researcher
  6. Bogdan Ostahie - Postdoc Researcher
  7. Stefan Stanciu - PhD Student

Research and Results:

A. Spontaneous symmetry breaking and the laser transition

The laser transition is one of the earliest examples of phase transition in driven, dissipative systems. As such it is also an example of transitions away from thermal equilibrium. This alone ensures the theoretical interest in the problem. Many numerical simulations in the literature aim at illustrating the phenomenon and at identifying a threshold point, but the problem cannot be decided except through an analytic proof. Indeed, numerical discretization is not able to prove a discontinuity, and a full coherence test for the emitted light involves an infinity of conditions on the infinite sequence of photonic autocorrelation functions.

The experimental situation is even more complicated. In general, instead of a sharp transition, one encounters a smooth, gradual change of regime, taking place on a whole interval of excitation strength. The journal Nature Photonics has even issued a laser "checklist" to ensure a certain standard in identifying laser operation.

We address the problem by examining the transition as an instability with respect to symmetry breaking, and discuss the advantages of this approach.

B. Dissipation effects and transport properties in quantum emitters

An optically active quantum dot (QD) confines charge carriers (i.e. electrons and holes) whereas a microcavity confines the optical modes (i.e. photons). The capability of positioning nanostructures such as quantum dots in a microcavity opens the way towards the manipulation of light-matter interaction. In this context we studied the transport and optical properties of a QD-cavity system coupled to source-drain contacts. As electrons/holes are injected into the conduction/valence states the excitonic states recombine and generate a net current across the dot. Besides the electron-hole recombination processes one cannot exclude photon losses in the cavity, described by a parameter κ and non-radiative recombination processes γ.

The populations of various many-body configurations (e.g exciton, trions, biexcitons) and the mean photon number are calculated from a Master equation which is derived in the dressed-states picture. We discuss the dependence of the steady-state current J_S on the cavity losses parameter κ, on photon number N collected within the cavity and on the coupling to the reservoirs Γ.

We find that the tunneling processes from and to the contacts are renormalized by the quantum dot-cavity coupling g_c. The Master equation is numerically solved for the s-shell many-body configurations of disk-shaped quantum dots. As long as the biexciton binding energy hampers the exciton recombination the dressed states made by the bright excitons and the biexciton are those of a three-level Λ-system. When fixing the couplings Γ to the particle reservoirs we find that the steady-state current exhibits van der Waals-like 'isotherms' as a function of the cavity losses parameter κ. In the strong coupling regime (g_c≫κ) the steady-state current J_S (κ) shows a non-monotonic behavior as a function of the cavity losses κ if the biexciton recombination processes are faster than the tunneling events. The current collects contributions from both positive and negative trion states.

The foreseen applications of electrical injection in optically active QDs embedded in a nanocavity include single-photon sources and more recently ground state electroluminescence.

C. Hund and anti-Hund rules in circular molecules

Accurate calculations of electronic spectrum in various nanostructures is a topic of constant interest both for understanding new physics and for applicative reasons.

We have studied molecules of circular shape (made either by atoms or by connected quantum dots -i.e. artificial molecules) with even number of electrons, the main question being whether the two top-most electrons occupy a Singlet or a Triplet state. In atomic physics, the Hund rule predicts always the state with the higher spin (Triplet) as ground state in such a case, according to Hund's first rule, but in different systems the answer is not a-priori known, justifying our study.

Both on-site (UH) and long range (VL) interactions have been considered within an extended Hubbard model. A special case is found for the 4N molecule at half filling, for which the first order energy correction (i.e. the exchange energy) vanishes and the second order gives always the singlet as ground state, and thus an anti-Hund situation. For all the other cases, the exchange energy does not vanish and its sign decides the ground state. In some instances the singlet ground state can be the ground state, if the long-range interaction exceeds a certain threshold as compared to the oh-site interaction. Thus, in some cases the system has an anti-Hund rule.

The results hold for arbitrary Hubbard or long range interactions, as well as for any number of atoms in the circular molecule. Such generality is owed to the fact that the singlet-triplet level spacing was analytically expressed in terms of the Fourier transform of the interaction potential.

Apart from providing detailed spectral calculations for molecules of potential interest, our studies may be also relevant for understanding various origins of non-trivial spin alignment.

Hund and anti-Hund rules in circular molecules
Dissipation e ffects and transport properties in quantum emitters
Spontaneous symmetry breaking and the laser transition


  1. Many-body effects in transport through a quantum-dot cavity system, I. V. Dinu, V. Moldoveanu, and P. Gartner
    Phys. Rev. B 97, 195442 (2018) - DOI:
  2. Hund and anti-Hund rules in circular molecules, M. Niţă, M. Ţolea, D. C. Marinescu, and A. Manolescu
    Phys. Rev. B 96, 235101 (2017) - DOI:


Dr. Paul Gartner

E-mail :

Postal address: Atomistilor street, no. 405A, Magurele, 077125, Romania