0.5 atoms improve the clock signal of 10,000 atoms

Transcription

1 0.5 atoms improve the clock signal of 10,000 atoms I. Kruse 1, J. Peise 1, K. Lange 1, B. Lücke 1, L. Pezzè 2, W. Ertmer 1, L. Santos 3, A. Smerzi 2, C. Klempt 1 1 Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D Hannover, Germany 2 INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy 3 Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D Hannover, Germany RTG-Workshop

2 Clock stability frequency instability 2

3 Outline Einstein-Podolsky-Rosen entanglement in quantum optics From quantum optics to atom optics Interferometer below the standard quantum limit Summary 3

4 Einstein-Podolsky-Rosen entanglement A. Einstein B. Podolsky N. Rosen quantum information quantum metrology [1] [2] [3] [4] /quantum-cryptography-with-conventional-lasers [5] 4

5 The Einstein-Podolsky-Rosen-Paradox p A p B = p A x A x 0 x B = x A + x 0 Heisenberg`s uncertainty priciple: ΔxΔp 1/4 A. Einstein B. Podolsky N. Rosen [1] [2] [3] 5

6 Inferred Heisenberg relation x B x est x A x A 2 Δ inf 2 x B Δ inf p B < 1 4 correlations in quadratures Reid, M. D. "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification." Physical Review A 40.2 (1989):

7 Quadratures Harmonic Oscillator EM wave many particle wave function electric field magnetic field 7

8 Measuring quadratures homodyne detection quadratures: x A/B = 1 2 a A/B + a A/B and p A/B = i 2 a A/B a A/B a L θ How to transfer - this into atom optics? a θ=0 θ=π/2 X A/B = x A/B cos θ + p A/B sin θ Ou, Z. Y., et al. "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables." Physical Review Letters (1992):

9 Outline Principle of interferometers Einstein-Podolsky-Rosen entanglement in quantum optics From quantum optics to atom optics Interferometer below the standard quantum limit Summary 9

10 From optical parametric down-conversion to spin dynamics 87 Rb F=1 m F = Optical parametric down-conversion Coherent pump Non-linear crystal Signal and idler beam Spinor Bose-Einstein condensate 87 Rb BEC in m F =0 Spin dynamics Atoms in m F =±1 10

11 Expected result m F = p A p B x A x B 11

12 Expected result m F = p A p B x A x B 12

13 Expected result m F = p A Δ 2 inf x B p B x A x B Δ 2 inf p B 13

14 Can it be a classic correlation? 2 non-classicalcorrelationswhen: Δ inf 2 x B Δ inf p B < 1 4 p A Δ 2 inf x B p B x A x B Δ 2 inf p B 14

15 Quadrature distributions Δ 2 inf x Δ 2 inf p Δ 2 inf p = V p = Var p A p B Inseparability: V x + + V p < 2 Δ 2 inf x = V + x = Var x A + x B EPR-entanglement: V x + V p < 1 4 Reid, M. D. "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification." Physical Review A 40.2 (1989):

16 How to measure quadrature distributions? θ A 1.8 MHz t LO θ A - m F = 1 q ΔE EPR state θ LO B - m F = 0 m F = 1 ΔE θ = θ A + θ B 500 Hz t θ B θ A time 16

17 Two-mode variances Local oscillator phase θ X A/B = x A/B cos θ π 4 + p A/B sin θ π 4 17

18 EPR criterion EPR: V x + V p < 1 4 Inseparability: V x + + V p < 2 Reid, M. D. "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification." Physical Review A 40.2 (1989):

19 Outline Einstein-Podolsky-Rosen entanglement in quantum optics From quantum optics to atom optics Interferometer below the standard quantum limit Summary 19

20 Principle of interferometers A B A θ B N A N B 20

21 Limits of interferometry for classical states: Standard quantumlimit (SQL) θ~ 1 N for entangled states: Heisenberg limit θ θ~ 1 N 21

22 Interferometry below the SQL A B A θ B N A N B 22

23 Interferometer below the SQL A B A θ B N A N B 23

24 Our Setup for an interferometer below the SQL A B 0.5 atoms A θ B N A N B 24

25 Three-mode interferometer π/2 T π/2 θ time 25

26 Three-mode interferometer π/2 π T π π/2 θ time 26

27 transferred fraction P Phase variation phase shift [π] microwave detuning [khz] 27

28 From three modes to two modes S A θ S = 1 2 ( ) A = 1 2 ( 1 1 ) θ 28

29 Single-mode squeezed states S = 1 2 ( ) x + p + A = 1 2 ( 1 1 ) x S x A p A x p S p x S x A J x N 2 x p S p A J y N 2 p 29

30 The interferometer on the Bloch-sphere 0 S 30

31 The interferometer on the Bloch-sphere 0 S 31

32 Variation of the local oscillator x p phase adjustment time [µs] Var P min = 2.25 db 32

33 transferred fraction P Interferometric stability phase shift [π] φ = P P/ φ P φ ideal = 0.5 P φ exp = microwave detuning [khz] Δφ = 1.5 db 33

34 Outline Einstein-Podolsky-Rosen entanglement in quantum optics From quantum optics to atom optics Interferometer below the standard quantum limit Summary 34

35 Summary EPR correlations with massive particles interferometer with a stability of 1.5 db below the SQL Thank you for your attention! 35

36 Quadratures... a L θ - beam splitter a Intensity measurement calculate difference classical local oscillator 36

37 Sub-shot noise frequency standard