IHP Quantum Information Trimester

1. Danish Quantum Optics Center University of Aarhus QuanTOp Niels Bohr Institute Copenhagen University Light-Matter Quantum Interface Eugene Polzik LECTURE 3 IHP Quantum Information Trimester

2. Einstein-Podolsky-Rosen (EPR) entanglement • Experimental techniques for observing quantum noise • and entanglement • Light • Photon statistics – dc measurements • Entanglement in • the spectral modes of light – ac measurements • Atoms • Addition of magnetic field – ac measurements with atoms • Generation of Entangled state of two distant Atomic Objects

3. L Simon (2000); Duan, Giedke, Cirac, Zoller (2000) Necessary and sufficient condition for entanglement • Einstein-Podolsky-Rosen paradox – entanglement; 1935 2 particles entangled in position/momentum

4. 2 particles entangled in position/momentum L 2d(X1- X2) 2d(P1+ P2) X1- X2 L P1+ P2 0 What does it mean in practice? • Prepare many identical pairs of particles • Measure X1- X2 on some of those pairs • Measure P1+P2 on others • Plot statistical distributions of the results • Measure the width of these distributions

5. Two independent particles Minimal symmetric uncertainties < d(P1+ P2)= d(X1- X2)= Entangled state X1- X2 P1+ P2 L 0 Why does it make sense?

6. Position – momentum uncertainty Macroscopic object – a mirror The best optical interferometry measurement: Assume M=1mg tough!

7. Instead of two EPR particles we use Two beams of light 1998 Two atomic ensembles 2001

8. Probability of counting n photons Compare to Variance: For coherent state Coherent state of light. Poissonian photon statistics. Delta-correlated noise.

9. coherent state (vacuum units) 1 -1 X 0 Measurements of quadratures Polarizing cube 450/-450 Polarizing cube Strong field A(t)

10. Phase squeezed Amplitude squeezed Quadrature operators. Squeezed light

11. Single photon state

12. RF spectrum analyzer Spectral measurements of Quadrature Operators Homodyne detector Polarization beamsplitter x

13. RF spectrum analyzer Flat spectrum of noise Delta correlated noise Spectral measurements on vacuum state (coherent state) Homodyne detector Polarization beamsplitter x vacuum

14. In real world Flat spectrum of noise Technical (classical) noise Quantum noise n > n > n > n

15. 1 MHz Same for sine modes Spectral measurements of Quadrature Operators Spectrum analyzer Advantage: getting rid of technical noise

16. Optical Spectrum of the strong field and the quantum field

17. Measuring rotating spin states B y z Atomic Quantum Noise 2,4 2,2 2,0 1,8 1,6 1,4 1,2 Atomic noise power [arb. units] 1,0 0,8 0,6 0,4 0,2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Atomic density [arb. units]

18. Detecting quantum projections of the spin in rotating frame Probe polarization noise spectrum 0,0008 B Atomic density (a.u.) probe Density [arb. units] ---------------------------------- 1.00 ± 0.02 0,0006 z 0.56 ± 0.01 0.21 ± 0.01 1.0 y 0.5 0.2 Noise power [arb. units] 0,0004 0,0002 Shot noise level , 0,0000 Larmor frequency W=320kHz 300000 310000 320000 330000 340000 RF frequency Frequency (Hz)

19. Entanglement of two distant macroscopic objects

20. L Simon (2000); Duan, Giedke, Cirac, Zoller (2000) Necessary and sufficient condition for entanglement • Einstein-Podolsky-Rosen paradox – entanglement; 1935 2 particles entangled in position/momentum

21. x y z y z x B. Julsgaard, A. Kozhekin and EP, Nature, 413, 400(2001) Experimental long-lived entanglement of two macroscopic objects. 1012 spins in each ensemble Spins which are “more parallel” than that are entangled

22. Z or Y 1st 2nd X Compare If the two macroscopic spins are collinear they must be entangled: Compare

23. Stern-Gerlach projection on any axis to x: Along y,z: ideally no misbalance between heads and tails of the two ensembles, or, at least, less than random misbalance 1+2 2 1 J J J

24. 2 gas samples 1012 atoms in each ensemble Cesium 4 3 6S 1/2 = - m ( 3 ,..., 3 )

25. x x Top view: y z z Therefore entangled state with Can be created by a measurement Total zandycomponents of two ensembles with equal and opposite macroscopic spins can be determined simultaneously with arbitrary accuracy Parallel spins must be entangled

26. How to measure the total spin projections? • Send off-resonant light through two atomic samples • Measure polarization state of light Duan, Cirac, Zoller, EP 2000

27. Entangling beam B B s+pump Y s- pump Z Entangled state of 2 macroscopic objects Y J1 Z J2 Polarization detection

28. And here is how to measure those sums... Sums of the transverse spin components are conserved by measurement

29. Jy1+ Jy2 0 Jz1+ Jz2 0 Establishing the entanglement bound Two independent ensembles Minimal symmetric uncertainties

30. Entanglement criterion: = 40 e s l u p e 30 b o r p e CSS h t f o 20 e c n a i r a v l a 10 r t c e p S 12 J [10 ] x 0 0 2 4 6 Collective spin of the atomic sample

31. < Entangled state Jy1+ Jy2 0 Jz1+ Jz2 0 Proving the entanglement condition:

32. J x2 s - Pumping beams J x1 s Optical Verifying Entangling + pumping pulse 0,6 pulse 0,4 0,2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Atomic density [arb. units] 700MHz 6 P PBS 3/2 Entangling and verifying beams out S y m =4 m =4 W = 325kHz F =4 6 S 1/2 F =3 Entangling and verifying pulses B -field Time 0.5 ms

33. Create entangled state and measure the state variance 2.0 1.5 Entangled spin states CSS 1.0 2 F x Atoms 0.5 e Light c (1pulse) S (1pulse) n y a 0.0 i r 0 2 4 6 a v l a r t c e p s d e S z (1pulse) i l y a m r o N 12 F [10 ] Collective spin of the atomic sample x Julsgaard, Kozhekin, EP Nature413, 400 (2001).

34. 1,00 0,95 0,90 Atom/shot(comp) / PN 0,85 0,80 0,75 0,70 0 2 4 6 8 10 12 14 16 Mean Faraday angle [deg] 10-12-2003/noise.opj Material objects deterministically entangled at 0.5 m distance Quantum uncertainty Niels Bohr Institute December 2003

35. Decoherence issues • only collective spin states are entangled • particles are indistinguishable -high symmetry of the system – • - robustness against losses. This is not a Schrodinger’s cat made of 1012 atoms! • no free lunch: • limited capabilities compared to ideal maximal entanglement Sources of decoherence: stray magnetic fields decoherence time 3 milliseconds collisions decoherence time 1-2 milliseconds

36. Phylosophical issues... Realism – two noncommuting spin components cannot be measured – therefore do not exist? But can be entangled Non-locality – two entangled macroscopic objects can be used to violate Bell-type inequalities via distillation All entangled Gaussian two-mode states are distillable (Giedke et al)