Atom Interferometry Measurements of Atomic Polarizabilities and Tune-out Wavelengths

Transcription

1 Atom Interferometry Measurements of Atomic Polarizabilities and Tune-out Wavelengths Alex Cronin, University of Arizona atom beam atom detector nanograting UVA Physics Colloquium March 18, 2016

2 Our Atom Beam Interferometer Space Domain Mach-Zehnder Nanogratings Slits 1G 2G 3G x 3 atom detector Oven x 2 x 1

3 Our Atom Beam Interferometer Space Domain Mach-Zehnder Nanogratings Slits 1G 2G 3G x 3 atom detector Oven x 2 Applications for Atom Interferometry: x 1 Inertial sensing: Atomic properties: Quantum phenomena:

4 Our Atom Beam Interferometer Space Domain Mach-Zehnder Nanogratings Slits 1G 2G 3G x 3 atom detector Oven x 2 Applications for Atom Interferometry: x 1 Inertial sensing: g, Ω, g, Ω, G, WEP tests, Grav. waves?, DE?, DDM? Atomic properties: α 0, t, <k D i>, f ik, C 6, α ω, λ zero, C 3, C 6, hyperpol. g? Quantum phenomena: (de)coherence, topological phases, h/m, a fs

5 Our Atom Beam Interferometer Space Domain Mach-Zehnder Nanogratings Slits 1G 2G 3G x 3 atom detector Oven x 2 Applications for Atom Interferometry: x 1 Atom interferometry s precision could make it the Swiss Army knife of physics -- Science News Inertial sensing: g, Ω, g, Ω, G, WEP tests, Grav. waves?, DE?, DDM? Atomic properties: α 0, t, <k D i>, f ik, C 6, α ω, λ zero, C 3, C 6, hyperpol. g? Quantum phenomena: (de)coherence, topological phases, h/m, a fs

6 Our Atom Beam Interferometer Space Domain Mach-Zehnder Nanogratings Slits 1G 2G 3G x 3 atom detector Oven x 2 x 1 1m photodiode atom beam 1G 2G Laser 3G atom detector

7 1G 2G (3G) Gaussian Schell Model (GSM) Atom Beam Simulations Parameters: atom ldb grating period Transverse coherence Longitudinal coherence Beam width db wavefront curvature PRA 78, (2008) PRA 89, (2014)

8 1G 2G (3G) Gaussian Schell Model (GSM) Atom Beam Simulations Parameters: atom ldb grating period Transverse coherence Longitudinal coherence Beam width db wavefront curvature PRA 78, (2008) PRA 89, (2014)

9 Nanograting w/ gap for C 3 expt 1 um

10

11 Atom Beam Interferometer Machine 1m intensity [kcounts/sec] C = 24.7% position [nm] Phase chopper Phase chopper

12 University of Arizona Atom Interferometry Laboratory Front Row (from left): Alex Cronin, Ivan Hromada, Raisa Trubko, Maxwell Gregoire Back Row (from left): Will Holmgren, James Greenberg

13 Atomic Polarizability (a) Experiment atom beam atom detector nanograting E-field gradient for a measurement f a

14 Tune Out Wavelength (l zero ) Experiment laser atom beam atom detector nanograting Interaction Laser for l zero measurement l zero

15 Van der Waals (C 3 ) Experiment atom beam nanograting Interaction Grating for vdw C 3 studies L R f vdw atom detector

16 Physics Motivations: Meas. of a(0) let us report lifetimes t, dipole matrix elements <k r i>, and f ik Combinations of C6 and a(0) measurements let us report a core Meas. of l zero let us report ratios of dipole matrix elements <P 3/2 r S 1/2 >/ <P 1/2 r S 1/2 > Meas. of a(0), C 3, and l zero probe different functions of oscillator strengths f ik

17 Measurements of a(0), C 3, and l zero probe different functions of atomic oscillator strengths f.

18 Measurements of a(0), C 3, and l zero probe different functions of atomic oscillator strengths f. l zero in more detail. a(w)=0 at w=2pc/l zero

19 Measurements of a(0), C 3, and l zero probe different functions of atomic oscillator strengths f. l zero in more detail. a(w)=0 at w=2pc/l zero

20 a [A 3 ] Year Author Historical measurements of a Cs a [A 3 ] Year Author a Cs

21 Historical polarizaility measurement techniques Beam deflection Miller and Bederson (1974) Hall and Zorn (1974) Interferometry Pritchard (1995) Vigue (2006) Vigue (2006) Hall and Zorn (1974)

22 Our 2010 E-field apparatus x Two paths through interferometer 1 E-fields cause a phase f for atom waves that depends on atomic polarizability a HV f a = d 2 v Differential phase shift f f 1 depends on a and v -2. y

23 Relative Contrast Phase shift Phase and contrast measurements with cylinder-plane electrodes φ = α V2 v 2 f(x) To report polarizability a Get f(x) from apparatus geometry. Beam position x (mm) Measure f and velocity distribution P( )

24 Our 2015 a(0) measurement apparatus: 2-cylinders & 2 phase choppers

25 Contrast measurements with cylinder-cylinder electrodes Contrast vs phase due to E-gradient enables measurement of W e to 5%, or gsinq to 2%. BS Thesis 2014 by James Greenberg Broad P(v) sharpens C peak Can measure both W e and g by using multiple v. Contrast loss can also affect Polarizability measurements E-gradient can improve dynamic range of aifm gyroscopes (Dispersion Compensation)

26 20 hours of velocity and a K measurements

27 3 methods to measure atom beam velocity Atom diffraction Phase Choppers Pulsed beam TOF

28 Pulsed atom beam velocity measurement with TOF TOF data Velocity distributions P(v) 0.8%

29 Counts/sec Atom beam velocity measurement with diffraction Atom beam Measure de Broglie wavelength using atom beam diffraction nanograting detector Rb K Na Detector position

30 Phase choppers for velocity measurement Pulsed electric fields periodically apply p phase shifts Interferometer contrast oscillates as we change the chopping frequency f Max contrast when f = n v/l = n f 0 Published in: Holmgren et al. NJP 2011

31 Velocity measurement with phase choppers Contrast (%) Cesium (3/17/2011) v 0 = (9) m/s r = 26.9(9) 0.06% 0 Phase shift (rad) Chopping frequency (khz) 12 14kHz

32 Error budget for Our 2015 polarizability Measurements.

33 2015 Results: a measurements for Cs, Rb, and K with 0.2% unc. Our measurements PRA 2015

34 2015 Results: a measurements for Cs, Rb, and K with 0.2% unc.

35 a Rb /a Na a b c n d q Arizona a Rb / a Na measurement f h i g j p a K / a Na a b c n d o e Arizona a k / a Na measurement f g i h j q p a Rb / a K a b n c g d f h i Arizona a Rb / a K measurement j k l m p = Holmgren et al. PRA 81, (2010) Our measured ratios of polarizabilities serve as a benchmark test for theoretical calculations [c]-[o]: [a] W.D. Hall and J.C. Zorn, PRA 10, 1141 (1974) [b] R.W. Molof, H.L. Schwartz, T.M. Miller, and B. Bederson, PRA10, 1131 (1974) [c]f. Maeder and W. Kutzelnigg, Chem. Phys. 42, 95 (1979). * [d] P. Fuentealba, J. Phys. B 15, L555 (1982). [e] W. Muller, J. Flesch, and W. Meyer, J. Chem. Phys. 80, 3297 (1984). [f] M. Marinescu, H.R. Sadeghpour, and A. Dalgarno, Phys. Rev. A 49, 5103 (1994). [g] S.H. Patil and K.T. Tang, J. Chem. Phys. 106, 2298 (1997). [h] I.S. Lim, et al., Phys. Rev. A 60, 2822 (1999). [i] M.S. Safronova, W.R. Johnson, and A. Derevianko, Phys. Rev. A 60, 4476 (1999). * [j] A. Derevianko, W.R. Johnson, M.S. Safronova, and J.F. Babb, Phys. Rev. Lett. 82, 3589 (1999). [k] J. Mitroy and M.W.J. Bromley, Phys. Rev. A 68, (2003). * [l] I.S. Lim, P. Schwerdtfeger, B. Metz, and H. Stoll, J. Chem. Phys. 122, (2005). [m] B. Arora, M.S. Safronova, and C.W. Clark, Phys. Rev. A 76, (2007). [n] E.-A. Reinsch and W. Meyer, Phys. Rev. A 14, 915 (1976). [o] K.T. Tang, J.M. Norbeck, and P.R. Certain, J. Chem. Phys. 64, 3063 (1976). [p] theory from DJSB99 without core electrons

36 Polarizability a in terms of oscillator strengths (f ik ), lifetimes (t), dipole matrix elements <k r i>, and line strengths S

37 Results based on our 2015 Polarizability measurements 4734(31) 3891(21)

38 Comparison to a(0) values inferred from other measurements

39 Combine our a(0) meas. w/ other lifetime meas. to report a r (0).

40 Combine C6 meas. w/ our a(0) meas. to report a r (0). C6 a(0)

41 Combine C6 meas. w/ our a(0) meas. to report a r (0). C6 a(0)

42 We thus meas. a r with <10% unc.

43 Static Dipole Polarizability SUMMARY: Measured a(0) for Na, K, Rb, Cs with 0.2% unc. Ratios with 0.1%. NEXT STEPS: SURPRISES: Listed in CRC handbook, sum-check MBPT calculations of <k r i> Use this method for Sr and Yb to improve atomic clocks Use Li and He* to anchor ratios Measure a(0) for molecules to test DFT Use E for dispersion compensation in gyroscopes / accelerometers Few ab initio theories are this accurate Several other experiments can be used to deduce a(0) Velocity measurements were challenging because E is a l db Lens We can report a core by combining measurements.

44 Precision Measurements of Tune-Out Wavelengths with an Atom Interferometer atom beam laser λzero nanogratings Raisa Trubko, Maxwell D. Gregoire, and Alexander D. Cronin College of Optical Sciences and Department of Physics University of Arizona DAMOP 2015

45 2015 Tune-Out Wavelength Measurement for K atoms theory other expt. UA atom interferometry expt. λ zero = (5) nm tune-out wavelength (nm) Source of error λ zero error (pm) laser wavelength 0.1 broadband light 0.3 laser polarization & lab rotation rate 0.2 Doppler shift 0.1 Mitroy 2013 RCICP Mitroy 2013 CICP (R=2) Arora 2011 MBPT-SD Arora 2011 no core Arora 2011 with (R=2) Johnson 1987 MBPT1 Johnson 1987 MBPT2 Volz 1996 lifetimes Wang 1997 photoas'n Falke 2006 mol.spect. Holmgren UA 2012 PRL Trubko UA 2015 Total systematic error Total statistical error Total error 0.5

46 Origin of tune-out wavelengths and motivation for measurements Potassium D2 D1

47 Origin of tune-out wavelengths and motivation for measurements

48 Origin of tune-out wavelengths and motivation for measurements D1 D2 D1 D2 D1

49 Origin of tune-out wavelengths and motivation for measurements D1 D2 D1 D2 D1

50 Science Impact and Experimental Sensitivities Comparison λ zero theory (nm) relative exper. uncertainty (pm) 7 Li (1) slope dα/dλ (a.u.) σ theory / σ experiment Δλ zero due to α core (pm) what we learn ,500, <0.01 Hyperpolarizability 39 K (3) , (1) R1 39 K (40) (4) R1, (core) 39 K (40) , (5) R2 & R3 87 Rb (7) 1.7 2, (1) R1, (core) 87 Rb (80) (7) R2, (R3 & core) 87 Rb (50) (1) Core & R3, (R2) 133 Cs (40) (2) R1, (core) 133 Cs (20) (6) R2, (R3, core) 133 Cs (30) (7) Core, (R2 & R3) 133 Sr (30) 2.6 1, (2) Intercom. f ik *Adapted from Cronin 2012 NSF proposal

51 Precision Measurements with Atom Interferometry atom beam nanogratings 100 nm position

52 Precision Measurements with Atom Interferometry atom beam laser nanogratings 100 nm position

53 Tune-out wavelength measurements with atom interferometry K D1 [1] William F. Holmgren, Raisa Trubko, Ivan Hromada, and Alexander D. Cronin, Measurement of a wavelength of light for which the energy shift for an atom vanishes, Phys. Rev. Lett. 109, (2012).

54 2015 Experimental Set-up laser system fiber wavemeter atom beam polarizer vacuum nanogratings atom detector 54

55 2015 Experimental Set-up laser system fiber atom beams wavemeter laser beam Optical cavity atom beam polarizer vacuum nanogratings atom detector 55

56 2015 Experimental Set-up laser system fiber wavemeter Optical cavity atom beam polarizer vacuum nanogratings atom detector 56

57 2012 and 2015 Tune-Out Wavelength Data

58 Doppler Shift & Wavemeter Calibration Decoherence Spectroscopy 0.22(5) pm shift

59 Doppler Shift & Wavemeter Calibration Decoherence Spectroscopy 0.22(5) pm shift

60 Measurement of broadband light from TA Laser etalon spectrometer

61 Error in λ zero due to broadband light from TA 0.1(3) pm shift

62 Error in λ zero due to elliptical polarization and Earth s rotation [2] Raisa Trubko et. al., Atom interferometer gyroscope with spin-dependent phase shifts induced by light near a tune-out wavelength, Phys. Rev. Lett. 114, (2015).

63 Rotation Rate Systematic Shifts in λ zero measurements due to laser polarization and magnetic field orientation circular polarization linear polarization λ zero right λ zero left 416 pm 64 pm 17 pm 2.6 pm

64 How rotation affects λ zero measurements Sagnac phase depends on atom velocity F S Physics: spin-dependent dispersion compensation Ingredients Atom beam with a spread in velocity

65 How rotation affects λ zero measurements Sagnac phase depends on atom velocity light-induced phase depends on atom velocity and spin F S Physics: spin-dependent dispersion compensation Ingredients Atom beam with a spread in velocity Atom beam with multiple spin states

66 How rotation affects λ zero measurements Sagnac phase depends on atom velocity light-induced phase depends on atom velocity and spin F S Physics: spin-dependent dispersion compensation Ingredients Atom beam with a spread in velocity Atom beam with multiple spin states Circularly polarized light Magnetic field parallel to optical k-vector

67 How rotation affects λ zero measurements Sagnac phase depends on atom velocity light-induced phase depends on atom velocity and spin F S F L m F = -2 m F = +2 Physics: spin-dependent dispersion compensation Ingredients Atom beam with a spread in velocity Atom beam with multiple spin states Circularly polarized light Magnetic field parallel to optical k-vector

68 2015 Tune-Out Wavelength Measurement for K atoms theory other expt. UA atom interferometry expt. λ zero = (5) nm tune-out wavelength (nm) Mitroy 2013 RCICP Mitroy 2013 CICP (R=2) Arora 2011 MBPT-SD Arora 2011 no core Arora 2011 with (R=2) Johnson 1987 MBPT1 Johnson 1987 MBPT2 Volz 1996 lifetimes Wang 1997 photoas'n Falke 2006 mol.spect. UA 2012 PRL UA 2015 Right & Left UA 2015 Right & Left average UA 2015 wavemeter & doppler UA 2015 broadband light Source of error λ zero error (pm) laser wavelength 0.1 broadband light 0.3 laser polarization & lab rotation rate 0.2 Doppler shift 0.1 Total systematic error Total statistical error Total error 0.5

69 Rb light-induced phase shift data

70 Tune-Out wavelengths l zero Measurement of λ zero lets us report R=(S D2 /S D1 )

71 = S D2 /S D1 = (13) In preparation (2016)

72 Tune-Out Wavelength Experiments: SUMMARY: Measured l zero = (5) for K with 0.5 picometer uncertainty Benchmark test for ratios of <4p J r 4s> calculated with MBPT Novel gyroscope demonstrated using l zero,lab NEXT STEPS: Other l zero will test other <k r i> Hyperpolarizability measurement idea intercombination line strength measurement for Sr clocks

73 Talk Summary: Polarizability ratios (e.g. ) measured with 0.1% uncertainty Tune-out wavelength l zero measured with 0.5 pm uncertainty C3 ratios (e.g. ) measured with 2% uncertainty. Each type of measurement tests different functions of atomic. Nanogratings work for several atomic species steps towards a universal atom interferometer

74 Atom interferometry studies of atomic structure Alex Cronin, University of Arizona John Perreault, PhD 2005 Ben McMorran, PhD 2009 Vincent Lonij, PhD 2011 Will Holmgren, PhD 2013 Ivan Hromada, PhD 2014 Raisa Trubko, current PhD student Maxwell Gregoire, current PhD student Robert Wild, BS 2004 Melissa Revelle, BS 2009 Cathy Klauss, BS 2011 James Greenberg, BS 2014 We acknowledge support from NSF Grant No New applications for atom interferometry with material gratings And a NIST PMG

75 Atom Interferometry: Swiss Army Knife of Physics

76 Thanks!