1. IOP, Bhubaneswar 22 nd Feb 2014 Prospect of using single photons propagating through Rydberg EIT medium for quantum computation Ashok Mohapatra National Institute of Science Education and Research, Bhubaneswar

2. Outline  Introduction to quantum computation using photons  Introduction to Rydberg EIT and its non- linearity  Our experimental progress at NISER  Conclusion

3. Classical computerQuantum computer Bit Qubit 0 or 1 Polarization states: |H> or |V> |  > =  1 |H> +  2 |V> 0 V or 5 V of a transistor output 2-level quantum system (e.g. Single photon) Classical gates AND, OR, NOT etc (Universal) Single qubit rotation operators and 2-qubit Controlled-NOT gate (Universal quantum gates) |α 1 | 2 +|α 2 | 2 =1

4. Qunatum computation using photons Single photon source Single photon detctors Optical elements for gate operation A Kerr non-linear medium for interactions of photons to devise a CNOT gate

5. Single qubit quantum gates Each photon as a qubit with two orthogonal polarized state Quarter wave plate Hadamard gate Half wave plate two Hadamard operation

6. CNOT gate: Interaction of photons Kerr non-linearity of a medium Increasing the length doesn‘t help due to strong absorption in the medium Electromagnetically Induced Transparency (EIT) provides a larger 3rd order non-linearity without absorption. where n 2 ≈ 10 -20 m 2 /W for typical glass

7. Electromagnetically induced transparency (EIT) Probe (Ω p ) F=2 F=1 87 Rubidium 5S 1/2 5P 3/2 F‘=3 nS 1/2 6 MHz

8. Electromagnetically induced transparency (EIT) 87 Rubidium 6 MHz 500 kHz Probe (Ω p ) F=2 F=1 5S 1/2 5P 3/2 F‘=3 nS 1/2 σ +σ + σ -σ - Coupling (Ω c ) EIT still doesn‘t provide enough non-linearity at single photon level

9. Rydberg EIT Rydberg EIT: Mohapatra et al., PRL, 98, 113003 (2007) (Thermal atoms) Weatherill et al., J. Phys. B, 41, 201002 (2008) (Cold atoms) 87 Rubidium 6 MHz 500 kHz Probe (Ω p ) F=2 F=1 5S 1/2 5P 3/2 F‘=3 nS 1/2 σ +σ + σ -σ - Coupling (Ω c ) Rydberg state

10. Rydberg atoms Size n 2 Dipole moment n 2 Lifetime n 3 Polarizability n 7 van der Waals n 11 Sensitivity to electric fields Scaling with principal quantum number n (low) Long lived 100 μsec for n > 40 Strongly interacting (QIP) Atom - atom interactions Rydberg states: large n Strong dipolar interaction Giant Kerr effect 5S 1/2 5P 3/2 5P 1/2 Few 100 nm

11. Rydberg Rydberg interaction Simplest case: van der Waals Atomic distance E Ω

12. Rydberg blockade Simplest case: van der Waals blockade condition few µm Atomic distance E Ω

13. Rydberg blockade ≡ Ω Urban et al., Nature Phys. 5, 110 (2009) Gaetan et al., Nature Phys. 5, 115 (2009) Wilk et al., Phys. Rev. Lett. 104, 010502 (2010)

14. Vogt et al., PRL 97, 083003 (2006) Heidemann et al., PRL 99, 163601 (2007) Raitzsch et al., PRL 100, 013002 (2008) Superatom

15. Non-linearity of Rydberg EIT 6 MHz 500 kHz Probe (Ω p ) F=1 Coupling (Ω c ) Rydberg state Dark state that doesn‘t couple to the probe beam and hence probe beam become transparent

16. Non-linearity of Rydberg EIT In the blockade sphere, more than one atom can not be excited which makes the dark state very fragile and get mixed with intermediate state. For large probe power, the EIT peak reduces with larger probe absorption. (a)One, (b) two, (c) three atoms per blockade sphere Durham university, UK group Pritchard et al. PRL, 105, 193603 (2010)

17. Non-linearity of Rydberg EIT (Pushing to single photon level) MIT group Peyronel et al. Nature, 488, 57 (2012)

18. Non-linearity of Rydberg EIT (Pushing to single photon level) MIT group, 2013, Firstenberg et al. www.nature.com/doifinder/10.1038/nature12512

19. Optical non-linearity of Rydberg EIT in thermal vapor Rydberg blockade radius is only scaled approximately by a factor of 3 in thermal vapor –Kuebler et al. Nature Photo. 4, 112 (2010) Optical pumping rate to the dark state is much faster than the transit time of the atoms

20. Measurement of the non-linear refractive index Rydberg EIT medium ω ω+δω+δ

21. ω ω+δω+δ

22. 5s 1/2 (F=3)→5p 3/2 (F’)→45d 5s 1/2 (F=3)→5p 3/2 (F’)→44s 5s 1/2 (F=3)→5p 3/2 (F’)→49d

23. Acknoledgement Arup Bhowmik (PhD) Sabyasachi Barik (Int. MSc) Surya Narayan Sahoo (Int. MSc) Charles Adams group at Durham University

25. Rydberg EIT with large probe power

26. EIT with large probe power

27. Rydberg EIT in thermal vapor

29. 44d EIT spectra Reference: Mohapatra et al. PRL (2007)

30. High precession spectroscopy (d - state fine structure splitting) Mohapatra et al. PRL 98, 113003 (2007). K. C. Harvey et al, Phys. Rev. Lett. 38, 537 (1977). W. Li, I. Mourachko, M. W. Noel, and T. F. Gallagher, Phys. Rev. A 67, 052502 (2003).

31. 5s 5p ns Giant Kerr effect of Rydberg EIT medium Electric field sensitivity of Rydberg state combined with the non-linear properties of EIT

32. Giant Kerr effect of Rydberg EIT medium 5s 5p ns ΔWΔW ∆W: 1.Stark shift by applying an external Electric field (DC Kerr effect) 2.Interaction induced shift (Similar to AC Kerr effect) (DC Kerr effect) Electric field sensitivity of Rydberg state combined with the non-linear properties of EIT

33. Experimental demonstration by phase modulation of light AOM + - Fast photodetector (1.2 GHz bandwidth) Spectrum analyzer

34. Phase modulation of light (Sideband spectra)

36. N-dependence of the Kerr constant α scales as n* 7 Ω c scales as n* -3/2 c 1 determines the absolute maximum c 2 determines the n* dependent scaling

37. Kerr effect in Rydberg EIT medium (Order of magnitude calculation) Gas (CO 2, 1 atm)B 0 ≈ 10 -18 m/V 2 WaterB 0 ≈ 10 -16 m/V 2 GlassB 0 ≈ 10 -14 m/V 2 NitrobenzeneB 0 ≈ 10 -12 m/V 2 Rydber dark state (thermal atoms)B 0 ≈ 10 -6 m/V 2 6 orders of magnitude bigger 10 orders of magnitude is expected for cold atoms

38. Noise spectra AOM Spectrum analyzer

39. More on Electro-optic and electrometry Electro-optic control of Rydberg dark state polariton Bason et al. PRA 77, 032305 (2008) Enhanced electric field sensitivity of rf- dressed Rydberg dark states (Bason et al. Bason et al. New J. Phys. 12, 065015 (2010)

40. Outlook QIP using thermal atoms in microcell –Quantum computation using photon –Single photon source –Quantum computation using mesoscopic ensemble of atoms Versatile electric field sensor THz imaging

41. Replace the EO crystal by Rydberg EIT in a microcell filled with thermal atoms (Preliminary idea)

42. Prof. C. S. Adams Dr. K. J. Weatherill Mr. M. G. Bason Mr. J. Pritchard Mr. R. Abel Durham University Group

44. Frequency stabilization of blue laser to a EIT peak using frequency modulation scheme (schematic) Toptica SHG @ 480 nm LP filter Toptica FALC module Fast feedback to master current (BW ~ 1 MHz) Slow feedback to master piezo PID Stabilized to Polarization spectroscopy ECDL @ 780 nm λ/2 λ/4 EOM Phase shifter 30 dBm power amplifier 20 dB amplifier Photodetector 1 MV/W, 10 MHz Di-chroic mirror Mixer Toptica DL pro

45. Home made EOM D. J. McCarron et al., Meas. Sci. Tech. 2008

46. Ultra-stable, no long term drift and 100 kHz of relative line- width observed with 1 μW of probe power Stabilization demonstrated for 26D 5/2 state by using less than 2 mW of blue light For 58D 3/2 state, less than 15 mW of blue light was used Abel et al, under preparation Frequency stabilization of blue laser to a EIT peak using frequency modulation scheme

47. Kerr effect in Rydberg EIT medium

48. In the regime

49. Kerr effect in Rydberg EIT medium In the regime

50. Kerr effect in Rydberg EIT medium Kerr effect (1875) In the regime

51. Measurement of the Kerr effect of Rydberg EIT medium 5p - 32s Jamin Interferometer

52. Measurement of the Kerr effect of Rydberg EIT medium + V - V 5p - 32s Jamin Interferometer Both the lasers are locked to the EIT signal Abel et al., submitted to Appl. Phys. Lett.

53. Measurement of the Kerr effect of Rydberg EIT medium

54. N-dependence of the Kerr constant

55. Sidebands on Rydberg dark states For small modulation frequency and Stark shift compared to any dipole allowed transition Ω=-1/2αE 2

56. Phase modulation of Rydberg dark states Ω/2

57. 2nd order sidebands

58. 1 st harmonic sidebands For an ac electric field (E 0 ) and dc field (E’)

59. 1 st harmonic sidebands For an ac electric field (E 0 ) and dc field (E’) 2 nd harmonic sidebands 1 st harmonic sidebands Application to precesion electrometry

60. Interaction of photons using EIT F=1 nS 1/2 Signal photon 1 Coupling

61. Interaction of photons using EIT F=1 nS 1/2 Large 3rd order non-linearity with less absorption But, still not enough to have π-phase shift to devise a useful phase gate at single photon level (Shapiro et al., PRA, 73, 062305 (2006)) Signal photon 1 Photon 2 Coupling