Cavity QED with single atoms

1. Quantum Optics and Spectroscopy Seminar Cavity QED with single atoms Single-atom laser and single-photon source Helena G. de Barros

2. Overview • Introduction • Part 1: Single-atom laser Experimental realization of a one-atom laser in the regime of strong coupling J. McKeever et al, Nature425,268 (2003). • Part 2: Single-photon source Deterministic generation of single photons from one atom trapped in a cavity J. McKeever et al, Science303,1992 (2004).

3. → Decay rate of the atom into free-space → Decay rate of the cavity field g → Rate of coherent atom-cavity field coupling H. J. Kimble, Physica ScriptaT76, 127 (1998) Hamiltonian neglecting losses: two-level atom free cavity field atom-cavity interaction → creation and annihilation operators for the single-mode of the cavity → Pauli operators Introduction Two-level atom in a cavity C → cavity resonance A → atomic resonance

4. Coherent coupling between the atom at a position  and the cavity mode, : Maximum rate at which one quantum of excitation is exchanged between atom and field. Rabi frequency : Weak coupling regime: Strong coupling regime: Introduction Strong coupling regime is such that is the volume of the cavity mode

5. TEM00 volume: → Finesse of the cavity Single quanta dominate the system dynamics. Introduction Relevant parameters Decay of the cavity field: Saturation photon number Cooperativity parameter In the strong coupling regime

6. Part 1: Single-atom laser Applications: Study quantum electrodynamics in the limit of single quanta

7. http://www.cco.caltech.edu/~qoptics/Poster/poster1.html Simplified Cs level scheme: F=3’ F=4’ 6P3/2 F=4 6S1/2 F=3 Probe DA Fig. 2 of PRL 90, 13 FORT DB Lock http://www.its.caltech.edu/~qoptics/cqed.html Part 1: Single-atom laser Experimental setup

8. Cavity length: Mode waist: µm µm Cavity Finesse: Trap depth: mK (47MHz) MHz MHz MHz Part 1: Single-atom laser Important numbers Typical lifetimes for a trapped atom in the presence of Ω3,4: 50 – 100 ms Strong coupling regime

9. Average of the total counting rate over 400 traces in function of time. Total counting rate for two different trapped atoms in function of time. Part 1: Single-atom laser Experimental results R → Total counting rate from DA and DB Overall detection efficiency:  = 0.05

10. → Mean intracavity photon number Output flux exceeds that from atomic fluorescence by more than 10 times. 6P3/2 6S1/2 Part 1: Single-atom laser Experimental results where No threshold Inferred intracavity photon number for two different ranges of pump intensity I3 (I4 is fixed to 13).

11. X=0.17 X=0.83 Normalized intensity correlation function for two different values of x. Part 1: Single-atom laser Normalized intensity correlation function x = 0.83 x = 0.83 Photon anti-bunching x = 0.17 x = 0.17 Sub-poissonian photon statistics

12. L = 2500 L0, n0 = 33.0 L = 100 L0, n0 = 1.32 L = L0, n0 = 0.013 L = L0, n0 = 0.013 L >> L0 Conventional lasers Part 1: Single-atom laser Theoretical analysis waist w0 constant L0 f xL0  → steady state solution of SEMICLASSICAL equations g(2)(0) andn / n0→ calculated from QUANTUM theory A. D. Boozer et al., Physical Review A70, 023814 (2004).

13. Part 1: Single-atom laser Summary • A strongly coupled one-atom thresholdless laser was reported. • The non-classical light exhibits photon anti-bunching and sub-poissonian photon statistics. • Theoretical calculations have been made to explore the behavior of the system when the length of the cavity was varied. These solutions were employed to investigate the passage from the semiclassical regime to the quantum domain.

14. Part 2: Single-photon source Applications: Quantum cryptography Linear Optics quantum computing

15. 3 → control pulse 4 → recycling pulse Part 2: Single-photon source Experimental setup

16. 4’ For each trapped atom: 3’ 4 g 3 4 3 Table of Efficiencies: Per trapped atom:  1.4  104 photons generated  350 photons detected Part 2: Single-photon source Pulse sequence Lifetime of the atom in the trap: around 140 ms

17. Part 2: Single-photon source Experimental results n(t) → Detection events from both detectors DA,B Single-photon pulse width = 120 ns P1(t) → Integrated probability of single detection P2(t) → Integrated probability of joint detection Probability of detecting a single photoelectric event in a trial = 2.84 % 16-fold suppression of coincidences relative to Poisson processes

18. Non-classical character  t The average area of the peaks around  = j t for j  0 exceeds the one for j = 0 by a factor of about R R(t) = 15.9  1.0. Part 2: Single-photon source Experimental results C() → cross-correlation between events from DA and DB → temporal separation between events detected at DA and DB  t= 10 µs is the repetition interval for generation of single photons. Time resolved coincidences as a function of .

19. R(t) Part 2: Single-photon source Excess of coincidences R0 is the ratio R(t) excluded the detector dark counts Hypothesis: Many events in which two atoms were trapped at the same time. Investigation: Monitor the evolution of the ratio R0 in function of the trapping time.

20. Evolution of the ratio R0 versus trapping time tT: • From the model: • ~ 3% of the trials are taken with two trapped atoms. • The generation of single photons succeeds with probability consistent to unity: g = 1.15  0.18. Average ratio of single- to two-photon event probabilities: R0 = 20.8  1.8 Part 2: Single-photon source Excess of coincidences The black points come from experimental data excluding detector dark counts. The red curve comes from their model that includes two trapped atoms. The blue dashed line represents the measured overall average of R0 for all tT.

21. Part 2: Single-photon source Summary • Deterministic generation of single-photon pulses by a single atom strongly coupled to an optical cavity was reported. • A 16-fold suppression of joint detection of events relative to a Poisson process was obtained. • The excess of coincidences was attributed to the rare two-atom events.