Conditional dynamics and quantum feedback, an experiment in cavity QED Luis A. Orozco UMD College Park Students: Matthew Terraciano Basudev Roy Michael Scholten Rebecca Olson Post Doctoral Associates: Dan Freimund Daniela Manoel Former Students: Joseph Reiner Wade Smith Stephan Kuhr (Bonn) Collaborators: Howard Wiseman, Griffith University, Brisbane, Australia. Perry Rice, Miami University, Oxford, Ohio. Julio Gea-Banacloche, University of Arkansas, Fayetteville, Arkansas Supported by NSF and NIST Open Quantum Systems in Quantum Optics The answer depends on how we probe the system Quantum Trajectories Strong coupling: The fluctuation is larger than the mean. (The smallest fluctuation is a photon). The signal is going to be noisy. For noisy signals: Make measurements in coincidence. Example: Handbury Brown and Twiss Calibration of a high energy detector. (Geiger in 1910 ) Hanbury-Brown and Twiss, (1956) Measure the size of a star by looking at coincidences of the intensity fluctuations. Michelson HBT Detector Source Field interference Intensity Coincidences Source A B A B time 4 coincidences out of 5 A detections; efficiency of B=4/5 It is not necessary to know the efficiency of A! Hanbury-Brown and Twiss Intensity-Intensity Correlations I (t ) I (t ) g ( ) ( 2) 2 I (t ) The correlation is largest at equal time g 2 (0) g 2 ( ) Schwarz Intensity correlation function measurements: ˆ ˆ I (t ) I (t ) g ( 2 ) ( ) 2 ˆ I (t ) Gives the probability of detecting a photon at time t + given that one was detected at time t. This is a conditional measurement: ˆ I ( ) g ( 2 ) ( ) c ˆ I Cavity QED Quantum Electrodynamics for pedestrians. No renormalization needed. A single mode of the electromagnetic field of a cavity. ATOMS + CAVITY MODE Non perturbative regime: Coupling > dissipation Dipole coupling between the atom d Ev and the cavity. g The field of one photon in a Ev cavity with Volume Veff is: 2 0Veff Cavity QED System g Cavity length 850 m , , 5.1, 3.7, 3.0 MHz 2 2 2 10-4 photons in the cavity in steady state. Steady State: Exchange of Excitation: Regression of the field to steady state after the detection of a photon. Each escape of a photon creates a very large disturbance. We want to monitor that disturbance or fluctuation. But we can only get one photon at best every time there is a disturbance. We have to average the conditional intensity. How does the data look in the lab? 7 663 536 starts 1 838 544 stops Non-classical, antibunched Conditioned measurements in the language of correlation functions allow the study of the dynamics of the system. Quantum conditioning, with photodetections, provides the most ideal times for controlling the evolution of the system. Feedback on a single photodetection. Quantum System Measurement Device Amplifier ENVIRONMENT We have to satisfy three conditions: Amplitude Sign of the step (parity) Time of the step We only have one bit of information, a click. We have good knowledge of the dynamics. Conditional dynamics of the system wavefunction 2g 2 pq 2 g2 q ss 0, g 1, g 0, e 2, g 1, e 2 a , p p( g , , ) and q q( g , , ) ˆ 2 gq a ss collapse 0, g pq 1, g ˆ 0, e 0, g f1 1, g f 2 0, e O 2 Field Atomic Polarization 2g Same coefficients when f 2 T f1 T Theoretical prediction. Convergence of the peak with increasing sample size. Error bars are 1 s. The horizontal line passes through thefinal measured value of the peak. Questions: How long can we hold the system and then release it? How sensitive is it to atomic detuning? Where is the information stored? What is quantum about this? Deterministic source? Can we feedback the field not the intensity? Feedback D = +2 MHz with detuning Atomic Resonance D = -2 MHz Cavity Resonance Semiclassical result, the feedback does not work! Answers: How long can we hold the system and then release it? As long as we want! How sensitive is it to detunings? With our protocol we only operate well on resonance. Where is the information stored? New steady state. What is quantum about this? The detection of the first photon. Deterministic source? No, we mostly create the vacuum: |0,g> + |1,g> + … Future directions: Cross correlations between field and atomic fluorescence can track the time evolution of the entanglement. We want to study this and started looking at a model for a single atom in the cavity. Construction is under way for the apparatus to measure it. We should be able to apply quantum feedback. Cross correlation between the fluorescence and the transmitted field. This function tracks the entanglement. Quantum trajectory of the atom field entanglement. The entanglement grows after a spontaneous emission! Summary: Knowledge of the conditional state for a continuously monitored cavity QED system Quantum feedback protocols We trigger on a fluctuation (photon detection) and change the drive at a particular delay after detection. Weak driving field manipulation. The initiation is with a fluctuation, the feedback is just as for any driven coupled oscillators.
Pages to are hidden for
"PowerPoint Presentation - Quantum Optics and Spectroscopy "Please download to view full document