The Josephson light-emitting diode

Transcription

1 Marseille, The Josephson light-emitting diode P. Recher, Yu.V. Nazarov, and L.P. Kouwenhoven, arxiv: Patrik Recher Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Germany

2 Motivation QD as single photon sources: - tunable light - photo emission at optical frequencies by demand P. Michler et al., Science 00; C. Santori et al., PRL 01 QD as source for entangled two photon cascade O. Benson et al., PRL 00; O. Gywat et al., PRB 02; N. Akopian et al., PRL 06 Semiconductor-superconductor junctions: (supercurrent through nanowires, creation of spin-entangled electrons) Doh et al., Science 05 P. Recher et al., PRB 01 J.A. van Dam et al., Nature 06 G.B. Lesovik et al., EPJB 01 Combination of superconductivity and optics?

3 Preliminaries Level coupled to normal leads: broadening t " t = 2#$ t 2 : tunneling rate " is DOS per spin in the lead

4 Level coupled to superconducting leads: coherent transfer of Cooper pairs " T 2e Amplitude: The phase factor T 2e " (1/2)# t e $i% in 2nd-order tunneling with T 2e << " exp("i#) is associated with creation of a Cooper pair in SC Note that SC stays in the ground state by transferring charge 2e, DOS of Cooper pairs is discrete => no broadening of level on QD

5 Effective model for QD level coupled to SC lead : induced pair-potential on QD = T 2e Diagonalization gives rise to 4 levels: doublet: and with energy

6 2 singlets: with with energy: and with energy: We have introduced standard BCS coherence factors: tunable by QD level energies (e.g. by gate voltage)

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8 p-n junction with SC leads " n - doped bandwidth p - doped electron level (energy ) and hole level (energy ) coupled to respective SC leads. Although bias voltage is applied, no charge transfer from n to p possible without annihilation of electrons and holes. z

9 Electron-hole recombination via emission of red photons ( heavy hole state)

10 Setup dynamics Cycle 1: Level structure of QD: Cycle 2: : mixed by superconductivity red photon emission proceeds along arrows (bold) leaving parity unchanged cycles connected by single-particle tunneling to/from SC leads (n-side brown, p-side green) + photon at emission rates smaller by factor

11 Biexciton-exciton cascade as an example normal state picture: transition rates: superconducting leads: depend on coherence factors!! => tunable by gate voltage Note: emission peak widths limited by emission time only! 8 distinct emission peaks in total QD state : has energy V eh V eh << " We thereby neglect possible interactions between electrons and holes which would not qualitatively change our results as long

12 Emission intensity of red photons Solving Master equation for QD states we can compute emission intensity : a) On resonance: We find three discrete peaks at shifted by induced gap and a continuous part (inset) due to quasiparticle creation in leads at Dashed curve is emission for normal leads in same regime b) General asymmetric case: (units of ) => 12 discrete peaks due to emission from both cycles

13 Correlated emission of photon pairs energy and spin correlated cycle 1 cycle 2 spin- but not energy-correlated finite spin on QD => (U=0) QD mostly in : Emission is correlated in polarization pairs (+,-) " polarization-entangled pairs

14 Josephson radiation at optical frequencies ---- emission of a single blue photon: photon! (not 2) How possible? At which frequency? Energy conservation requires Hamiltonian destroys one electron-hole pair with each emitted photon. => need annihilation without emission => static electric field with

15 rate for emission of single blue photon (polarization ): To second order in Note that at Then:, emission is coherent, i.e. phase difference between SCs

16 Probe coherence with SQUID with interference contribution periodic in flux through SQUID with period

17 Intensity at Josephson frequency (for both QDs) d : E 0 : Dipole moment of QDs Static electric field (in-plane) QD2

18 Conclusions Setup where electron level and hole level in QD coupled to SC leads Emission proceeds in several discrete peaks at frequencies as well as a continuous tail at characteristic of induced superconductivity in QD Coherent coupling to SCs allows to tune the correlated 2 photon emission cascade photons at Josephson radiation are coherent and reminiscent of

19 Energetics even-parity cycle

20 Process of blue -photon emission 2eV sd ev sd even-parity cycle 0

21 Setup dynamics Cycle 1: : mixed by superconductivity Cycle 2: red photon emission proceeds along arrows (bold) leaving parity unchanged cycles connected by single-particle tunneling to/from SC leads (n-side brown, p-side green) + photon at emission rates smaller by factor