1. A. Imamoglu Department of Electrical and Computer Engineering, and Department of Physics, University of California, Santa Barbara, CA 93106 Quantum Dot Single-Photon Source: Prospects for Applications in Quantum Information Processing Outline 1) Quantum dots 2) Properties of quantum dot single photon sources 3) High efficiency photon counters Co-workers A. Kiraz, J. Urayama, B. Gayral, C. Becher, P. Michler, C. Reese, L. Zhang, E. Hu W.Schoenfeld, B. Gerardot, P. Petroff

2. Requirements for linear optics quantum computation (LOQC) Linear optical elements: beam-splitters, polarizers, lenses optical delay/memory Single-photon sources: indistinguishable single-photon pulses on demand (with efficiency > 99%) Photon counters: high-efficiency detectors with single-photon discrimination  Appears to avoid the very demanding requirement for large (coherent) photon-photon interactions.

3. Single Photon Sources Single atom in a cavity: Rempe et al. PRL (2002) Single nitrogen vacancy in diamond: H. Weinfurter et al. PRL (2000) P. Grangier et al. PRL (2002) Single Molecule at room temperature: B. Lounis and W.E. Moerner, Nature (2000) Single InAs Quantum Dot in a microcavity: P. Michler et al., Science 290, 2282 (2000) C. Santori et al., PRL 86, 1502 (2001) Z. Yuan et al., Science 295, 102 (2002) A regulated sequence of optical pulses that contain one-and-only-one photon

4. What is the signature of a single-photon source? Intensity (photon) correlation function:  gives the likelihood of a second photon detection event at time t+ , given an initial one at time t (  ).

5. What is the signature of a single-photon source? Intensity (photon) correlation function: Experimental set-up for photon correlation [g (2) (  )] measurement: Records the waiting-time between the successive photon-detection events at the two detectors (APD).  gives the likelihood of a second photon detection event at time t+ , given an initial one at time t (  ).

6. Signature of a triggered single-photon source Triggered single photon source: absence of a peak at  =0 indicates that none of the pulses contain more than 1 photon. Signature of a triggered single-photon source Intensity (photon) correlation function:  gives the likelihood of a second photon detection event at time t+ , given an initial one at time t (  ). g (2)   0

7. Quantum Dots Artificial structures that confine electrons (and holes) in all 3 dimensions. Atoms Quantum dots (QD)  Quantized (discrete) eigenstates in both cases (  0D density of states). V atom (x) V QD (x)  E QD  E atom  Å  Å  E atom  ~ 1–10 eV >> kT room = 26 meV  E QD ~ 1–100 meV ~ kT room ! Unlike atoms, QDs are sensitive to thermal fluctuations at room temp.

8. Quantum Dots vs. Atoms Strongly trapped emitters: QDs do not have random thermal motion. Easy integration in nano-cavity structures. Strong coupling to optical fields: QD oscillator strength f ~ 10 – 300 (collective enhancement). Electrical injection of carriers (electrons and holes). Each QD has a different resonance (exciton) energy. Difficult to tune QDs into resonance with cavity modes.

9. Self-Assembled InAs Quantum Dots Atom-like characteristics of Quantum Dots: sharp emission lines photon antibunching  artificial atom for T < 77 K! Quantum dots appear spontaneously due to lattice mismatch, during MBE growth. AFM of InAs QDs 2 μm Each quantum dot is different

10. A single InAs Quantum Dot Two principal emission lines from lowest energy s shell 1X radiative recombination of a single e-h pair in the s-shell (exciton) 2X radiative recombination when there are two e-h pairs in the s-shell (biexciton) Due to carrier-carrier interaction Typically h 1X = h 2X + 3 meV -- - + ++ non-resonant laser excitation phonon emission GaAsInAs GaAs exciton emission (1X)

11. Photon correlation of a single-photon source  all peaks in G (2) (  ) have the same intensity  pulsed coherent light

12. Photon correlation of a single-photon source Pump power well above saturation level  all peaks in G (2) (  ) have the same intensity  pulsed coherent light  the peak at  =0 disappears.  single photon turnstile device with at most one photon per pulse Photon correlation of a single-photon source

13. Turnstile Device at Different Pump Powers  Lower pumping power has the same effect as loss in the optical path well below saturation onset of saturation well above saturation Turnstile Device at Different Pump Powers

14. No roughness on the sidewall up to 1nm ! Q>18000 for 4.5  m diameter microdisk Q=11000 for 2  m diameter microdisk Fundamental whispering gallery modes cover a ring with width ~ /2n on the microdisk Microdisk Cavities Photoluminescence from a high-QD density sample substrate GaAs AlGaAs GaAs substrate GaAs AlGaAs GaAs Q>18000

15. A single quantum dot embedded in a microdisk Pump power well above saturation level Q = 6500 Larger width of the peaks due to longer lifetime of the quantum dot P=20W/cm 2 T=4K

16. Tuning the exciton into resonance with a cavity mode T=44K Small peak appears at  =0 Peaks in G (2) (  ) are narrower:  Purcell effect ? Cavity coupling can provide better collection

17. Quantum dot lifetime measurement  Time-correlated single-photon counting experiments show no temperature dependence for exciton lifetime.  First direct measurement of Purcell effect (F P  2) for a single quantum dot.

18. Purcell Effect: cavity-induced decay When an emitter is placed inside a high-Q, low volume cavity, there are two channels for radiative decay: i) spontaneous emission into vacuum modes (  spon ) ii) irreversible emission into the cavity mode (g 2 /  cav ) – scales as Q/V eff  Purcell effect: g 2 /  cav >  spon Purcell effect in a single photon source i) Fast emission  reduced jitter in photon emission time. ii) Emission predominantly into a single cavity mode  high collection efficiency. iii) Reduced sensitivity to dephasing  Transform limited (indistinguishable) photons in the good-cavity limit: g 2 >  cav  dep  Purcell effect is essential for applications in linear optics quantum computation.

19. Linear optics quantum computation (LOQC) Key step is two-photon interference on a beam-splitter:  in   out   g 34 (2) (  =0) = 0  Requires that the two incident photons have the same spatio-temporal profile: single photon pulses have to be transform-limited. For LOQC we need (?) g 34 (2) (  =0) < 0.01 [ Santori et al. observed g 34 (2) (  =0) = 0.3 using resonant excitation] E3E3 E2E2 E1E1 E4E4 No coincidence detection for indistinguishable photons Linear optics quantum computation (LOQC)

20. Can we use QD single-photon source in LOQC? High single-photon collection efficiency (  ~ 44%) has been demonstrated using the Purcell effect (Gerard et al., Pelton et al.):  F P ~ 10 gives   90% and photon emission time  sp ~ 100 psec. Even under resonant p-shell excitation, we have jitter in photon emission time ~ 10 psec:  Coincidence count-rate in two-photon interference will be ~ 10%, since information about the single-photon pulse can be obtained from the emitted phonon(s).  The requirements for high collection efficiency and complete indistinguishability are incompatible (even in the good-cavity limit)! resonant laser excitation phonon emission Can we use QD single-photon source in LOQC?

21. Photon counting using stored light It is possible to map the quantum state of a propagating light pulse onto metastable collective excitations of an atomic gas, using electromagnetically induced transparency (EIT).  # of incoming photons = # of atoms in the (hyperfine) excited state. State-selective fluorescence measurements (developed for trapped ions) can achieve efficiencies > 99% in measuring the number of atoms/ions in a given state – without requiring high efficiency photon detection.  By combining these two techniques, we could realize a photon counter with efficiency > 99%.

22. Storing light using electromagnetically induced transparency (EIT) signal pulse i) coupling laser on EIT medium coupling laser F=2, m F =2 F=1, m F =1 signal pulse ii) coupling laser on; signal pulse inside the medium # of atoms in state | F=2,m F =2> = # of initial signal photons Stored signal pulse (dark polariton) iii) coupling laser off

23. Measuring photon number using EIT stored singal pulse (dark polariton) detection laser EIT medium scattered photons detection laser F=3, m F =3 F=2, m F =2 F=1, m F =1