1. Squeezed Light and Quantum Imaging with Four-Wave Mixing in Hot Atoms

2. Alberto Marino Ulrich Vogl Jeremy Clark (U Maryland) Quentin Glorieux Neil Corzo Trejo (CINVESTAV, Mexico) Ryan Glasser PDL Zhifan Zhou (ECNU) Andrew Lance (Quintessence Labs) Raphael Pooser (Oak Ridge) Kevin Jones (Williams College) Vincent Boyer (Birmingham) Atomic Physics Division National Institute of Standards and Technology Gaithersburg, MD also with the Joint Quantum Institute (NIST/U Maryland) $ JQI NSF-PFC, DARPA, AFOSR $ Squeezed Light and Quantum Imaging with Four-Wave Mixing in Hot Atoms

3. something for (almost) everyone squeezed light –bright beams –vacuum slow light continuous-variable entanglement images (multiple-spatial-mode) narrowband at Rb color (atom optics) relatively simple experiments! really cool! if only this were 20 years ago! squeezed light from 4WM in Rb vapor

4. First observations of squeezed light in 1985 (Slusher, et al.) were based on degenerate 4WM in atomic vapors. Most experimental reports of squeezing by 4WM in atomic vapors were published more than 10 years ago... mostly based on 2-level systems; these ended with several attempts in cold atom samples. Most recent squeezed-light results use OPO’s and OPA’s with  (2) materials in a cavity; strong squeezing achieved. 4WM in fibers generates correlated photons and ~7 dB of squeezing. Lots of theoretical examinations...... but none that actually predicted squeezing under our conditions. history

5. We are trying to perform quantum optics and “quantum atom optics” experiments: create non-classical photon beams that can, in turn, be used to produce non-classical atom beams. also try to do “real” quantum optics and image processing experiments with non-classical light amplifiers. Goals

6. Raman transition 0k0k 2k2k k laser kiki kk k1k1 k2k2 kk kk √2/2  k k1k1 “dress” the atoms in the BEC with the “downward-going” frequency of a Raman transition drive the “upward-going” transition with correlated photon beams k2k2 twin beams of atoms out k laser BEC Producing correlated atoms from correlated photons P. Lett, J. Mod Opt. 51, 1817 (2004)

7. Single-mode squeezing

8. p1p1 x1x1 p2p2 x2x2 Coupled Gain correlations two vacuum modes two noisy, but entangled, vacuum modes Two-mode squeezing: phase-insensitive amplifier

9. Squeezing quadratures

10. squeezing from 4WM in hot Rb vapor 85 Rb in a double-  scheme ~120 C cell temp. ~1 GHz detuned ~400 mW pump ~100  W probe - narrowband - no cavity

11. strong intensity-difference squeezing measured 1 MHz detection frequency RBW 30 kHz VBW 300 Hz pump detuning 800 MHz Raman detuning 4 MHz

12. noise “squeezed light” implies, in some form, reduced fluctuations this is usually compared to “shot noise” N particles/second => noise ~ N 1/2 state of the art; (linear and log) 3 dB = factor of 2; 10% noise = -10 dB Two-Mode: We have -8.8 dB (13% of “shot noise”) “project” lossless squeezing level of -11 dB at source world record (using an OPO): -9.7 dB (11%) twin beam; -11.5 dB for single-mode quadrature squeezing We have -3 dB of single-mode squeezing previous best with 4WM in atoms: -2.2 dB LIGO will use -6 dB of squeezing in phase II

13. intensity-difference squeezing at low frequencies better than 8 dB noise suppression if backgrounds subtracted!

14. image correlations no cavity means fewer constraints on modes!

15. image correlations in space pump relic amplified probe (spatially filtered + ) generated conjugate (spatially filtered) expect that correlations are “reflected” radially through the pump note that “images” do not constitute multiple spatial modes! 4.7 dB intensity difference squeezing between images at 1 MHz

16. phase stable local oscillators at +/- 3GHz from the pump demonstrating entanglement pump probe conjugate pzt mirror pzt mirror + or - scan LO phase alignment and bright beam entanglement

17. demonstrating entanglement pumps probe conjugate LO pump pzt mirror pzt mirror + and - scan LO phase signal pump 50/50 BS vacuum squeezing unsqueezed vacuum

18. measurements at 0.5 MHz “twin beam” vacuum quadrature entanglement

19. entangled images measurements at 0.5 MHz V. Boyer, A.M. Marino, R.C. Pooser, and P.D. Lett, Science 321, 544 (2008).

20. cone of vacuum-squeezed modes (allowed by phase matching) seeded, bright modes

21. entangled “images” arbitrarily-shaped local oscillators can be used (we used a “T”-shaped beam) squeezing in both quadratures; (equivalent results in all quadratures) Gaussian bright-beam (-3.5 dB) or vacuum (-4.3 dB); T-shaped vacuum (-3.7 dB) implies EPR-levels of CV-entanglement could be measured in each case no feedback loops or mode cleanup cavities!

22. Images no cavity, so freedom for complex and multiple spatial modes!

23. phase-sensitive amplifier the phase of the injected beam, with respect to those of the pumps, will determine whether the beam will be amplified or de-amplified One can design an amplifier for given field quadratures - useful for signal processing! ++ -- 00 given the phase of 3 “input” beams the 4th phase is free to adjust for gain -- 00 ++  + = 2  0 -  - 0 = 2  0 -  - -  + phase-insensitive phase-sensitive no free parameters gain:

24. phase-sensitive amplifier set-up ti:sapph laser Double-pass semiconductor tapered amp Double-pass 1.5 GHz AOM ~1 mW ~ 500 mW Rb cell optics pzt for phase lock Phase lock each pump beam to the probe. -3 GHz +3 GHz probe

25. problems - tapered amps noisy; astigmatic output beams; feedback adds laser noise - detuning needs to be large to avoid other 4WM - 500 mW is marginal power - non-co-linear geometry helps separate the beams but makes the (distorted) wavefronts not match (getting a fixed phase for amplification is hard) phase relation varies across probe beam (phase fronts are distorted)

26. competing 4WM processes pump 1pump 2 “probe” “extra conjugate” extra 4WM can be suppressed by putting “pump1” mid-way between the absorptions (more power needed)

27. Experimental Setup - PSA Double Lambda Scheme in 85 Rb Experimental Parameters Pump ~200mW each Probe ~ 0.1mW Cell ~12mm Gain ~ 2 Angle ~ 0.5° Orthogonal Linear Pol. Cell Temperature 86 C The probe gets amplified or deamplified depending on its phase. Pumps Probe 5S 1/2 5P 1/2 3GHz Probe

28. “single mode” quadrature squeezing PSA (phase-sensitive amplifier) homodyne detection direct detection squeezing calculated from probe gain lower cell temp ~90 C than for phase- insensitive case seeded “vacuum seeded”

29. Vacuum Squeezing Squeezing trace at 1 MHz (zero span, RBW: 30 KHz, VBW: 100 Hz) for the vacuum squeezed state, normalized to the shot noise. One-photon detuning 0.8 GHz. Two-photon detuning 4MHz.

30. Vacuum Squeezing vs Pump Power Squeezing [dB] Squeezing at 1 MHz (zero span, RBW: 30 KHz, VBW: 100 Hz) for the vacuum squeezed state, normalized to the shot noise. One-photon detuning 0.8 GHz.

31. Vacuum Squeezing Bandwidth

32. Squeezing trace (RBW: 10 KHz, VBW: 100 Hz) for the vacuum squeezed state, normalized to the shot noise. One-photon detuning 0.8 GHz. Two-photon detuning 4MHz. Pump1 = 225 mW. Pump 155mW.

33. Vacuum Squeezing Bandwidth Squeezing trace (RBW: 10 KHz, VBW: 100 Hz) for the vacuum squeezed state, normalized to the shot noise. One-photon detuning 0.8 GHz. Pump1 = 225 mW. Pump 155mW.

34. Vacuum Squeezing Bandwidth Squeezing trace (RBW: 10 KHz, VBW: 100 Hz) for the vacuum squeezed state, normalized to the shot noise. One-photon detuning 0.8 GHz. Pump1 = 225 mW. Pump 155mW.

35. Vacuum Squeezing Bandwidth Squeezing trace (RBW: 10 KHz, VBW: 100 Hz) for the vacuum squeezed state, normalized to the shot noise. One-photon detuning 0.8 GHz. Pump1 = 225 mW. Pump 155mW.

36. phase-sensitive amplifier To avoid other phase-insensitive 4WM processes the detuning is much different than with the phase- insensitive version of the 4WM amplifier. These processes can be suppressed, however, not completely. This leads to excess noise and limits the gain at which the PSA can be operated. It still operates with multiple spatial modes, but the symmetry of the spatial modes will be an issue to some (unknown) extent.

37. multi-spatial mode “single-mode quadrature squeezing” attenuating beam (modes) by blocking in different manners

38. Summary 4WM should add to our ability to perform quantum imaging and amplifier experiments narrowband source should allow us to use this to interface with Rb atom quantum memories

39. group photo Ulrich Vogl Ryan Glasser Jeremy Clark Quentin Glorieux Zhifan Zhou Neil Corzo Trejo Alberto Marino