1. || Quantum Systems for Information Technology FS2016 Quantum feedback control Moritz Businger & Max Melchner06.05.20161

2. || Quantum Systems for Information Technology FS2016 Introduction  Introduction to QND  Feedback control  State correction with coherent fields  State correction with single-photon actuators  Feedback results  Improvements/Applications Moritz Businger & Max Melchner06.05.20162

3. || Quantum Systems for Information Technology FS2016 Introduction to QND Off-resonantresonant π-Pulse-State flip π/2-PulseQNDEntanglement R1R1 R2R2 Moritz Businger & Max Melchner06.05.20163

4. || Quantum Systems for Information Technology FS2016 Feedback control Moritz Businger & Max Melchner06.05.20164

5. || Quantum Systems for Information Technology FS2016 Feedback control Moritz Businger & Max Melchner06.05.20165

6. || Quantum Systems for Information Technology FS2016 Feedback control Moritz Businger & Max Melchner06.05.20166

7. || Quantum Systems for Information Technology FS2016 Quantum Feedback control  Initializing a Fock state  Stabilizing a Fock state  Lifetime of a Fock state: T n = T c /n where T c = 65 ms and with a repetition time of T a = 82 μs, this gives us ~1000 measurements per decay Moritz Businger & Max Melchner06.05.20167

8. || Quantum Systems for Information Technology FS2016 1 2 3 1.Measurement of the cavity state 1.Comparison to the target state 1.Field translation by emission of coherent field Moritz Businger & Max Melchner06.05.20168 Part 1: Coherent field actuator

9. || Quantum Systems for Information Technology FS2016 Measurement of the cavity state Projection caused by the measurement: ρ → M j ρM j T /Tr(ρM j † M j ) (j=e,g) M g =sin[Φ r +Φ 0 (N+1/2)/2] M e =cos[Φ r +Φ 0 (N+1/2)/2] Weak Quantum nondemolition (QND) Measurement  Ramsey measurement with an atom- cavity detuning Δ/2π = 245 kHz  P(e) = Cos 2 (Φ + nΦ 0 ) Φ 0 = 0.256π Moritz Businger & Max Melchner06.05.20169

10. || Quantum Systems for Information Technology FS2016 Comparison to the target state Moritz Businger & Max Melchner06.05.201610 Calculation of ρ:  Previous state  Projection of the measurement  g, e, 0, gg, ee, eg, ge  Evolution of the cavity during measurement time

11. || Quantum Systems for Information Technology FS2016 Field translation by the actuator Actuator action:  of the field in the cavity by: D(α)=exp(αa † -α*a)  Where α is chosen by K such that it minimizes d(ρ t,D(α)ρD(-α))  d = 1-Tr(Λ (n_t) ρ) Moritz Businger & Max Melchner06.05.201611

12. || Quantum Systems for Information Technology FS2016 Measurement results Moritz Businger & Max Melchner06.05.201612

13. || Quantum Systems for Information Technology FS2016 1) No Feedback2) With Feedback Moritz Businger & Max Melchner06.05.201613

14. || Quantum Systems for Information Technology FS2016  Rydberg atoms act as probes and as actuators, depending on their detuning  Fock state stabilization is done by single-photon actuators Experimental Setup Moritz Businger & Max Melchner06.05.201614 Part 2: Single-Photon Actuators

15. || Quantum Systems for Information Technology FS2016  When the Control decides to send a probe, the atoms are detuned (using V) and the microwave pulses (S1 & S2) are set to π/2  When the control decides to send an emitting actuator, the atoms are tuned to resonance and S1 emits a π-pulse, S2 is turned off  When the control decides to send an absorbing actuator, the atoms are tuned to resonance and S1 & S2 are turned off Moritz Businger & Max Melchner06.05.201615 Probe/Actuator preparation

16. || Quantum Systems for Information Technology FS2016 Probe/Actuator preparation Actuator preparation (Δ=0) Probe preparation(g 2 /Δ << 1) Moritz Businger & Max Melchner06.05.201616

17. || Quantum Systems for Information Technology FS2016  Cavity Phase Shift (phase shift per photon) is adjusted such that 8 different photon states can be distinguished  Rydberg atoms are created every 82µs  K tries to minimize d = Σ n (n − n t ) 2 p(n) Moritz Businger & Max Melchner06.05.2016 Stabilization of n t = 4 Fock state. 17 Feedback parameters

18. || Quantum Systems for Information Technology FS2016 Moritz Businger & Max Melchner06.05.2016 [2] 18 Feedback parameters Stabilization of n t = 4 Fock state.  Stabilization over 140 ms (compared to Fock state lifetime of ~ 10 - 60 ms)  There is no limit on stabilization time!  When n < n t − 0.4, K programs emitter samples  When − 0.4 ≤ n ≤ n t + 0.6, K decides to send sensor samples

19. || Quantum Systems for Information Technology FS2016 (a)Poisson Distribution with n t photons on average (b) Distribution after 140 ms of Feedback (c) Distribution after K determines p(n t ) > 0.8 [2] Moritz Businger & Max Melchner06.05.201619 Feedback results

20. || Quantum Systems for Information Technology FS2016  Stabilization using single-photon actuators (quantum vs. classical actuators)  Convergence time to target Fock state is halved  More efficient stabilization, no unnecessary excitations  Fock state sequence can be programmed Moritz Businger & Max Melchner06.05.201620 Differences to first paper

21. || Quantum Systems for Information Technology FS2016  Weak coupling (~10-100 kHz)  Low transmissivity (~1-10 Hz)  No transmission measurement  States with n > 3 can only be stabilized up to about p(n) = 0.6  Small detection efficiency (~0.3) Moritz Businger & Max Melchner06.05.201621 Difficulties

22. || Quantum Systems for Information Technology FS2016  Higher repetition rate allows for stabilization of larger Fock states  Implement transmission measurement of cavity  Same procedure is in principle possible in any resonator/qubit system  Higher coupling rate allows for shorter interaction time  Read-out with single qubit possible in a circuit QED setup Moritz Businger & Max Melchner06.05.201622 Improvements

23. || Quantum Systems for Information Technology FS2016  Feedback procedure allows for correction of spontaneous emission  Computing with photon number states  Study of quantum/classical boundary  Superpositions of Fock states can be used for quantum computing (quantum storage) Moritz Businger & Max Melchner06.05.201623 Potential Applications

24. || Quantum Systems for Information Technology FS2016 [1] C. Sayrin, I. Dotsenko. Real-time quantum feedback prepares and stabilizes photon number states. Nature 477, 73–77, 2011 [2] X. Zhou, I. Dotsenko. Field locked to Fock state by quantum feedback with single photon corrections, 2012, arXiv:1203.1920 References Moritz Businger & Max Melchner06.05.2016 24 References

25. || Quantum Systems for Information Technology FS2016  Long lifetime  Large electric dipole moment allows for observation of single-photon interactions  GHz transitions allow for coupling to superconducting microwave resonators  Easy qubit tunability using electric fields (Stark shift)  Circular states have small linewidths ((n+1,n,n) -> (n,n-1,n-1)) Moritz Businger & Max Melchner06.05.201625 Advantages of Rydberg Atoms