Hong Ou Mandel experiment with atoms

BEC on an MCP Hong Ou Mandel experiment with atoms Chris Westbrook Laboratoire Charles Fabry, Palaiseau FRISNO 13, Aussois 18 march 2015

2 particles at a beam splitter 1 particle at each input 4 possibilities: d a c b both transmitted both reflected both in c both in d

2 particles at a beam splitter 1 particle at each input 4 possibilities: d a c b both transmitted both reflected both in c both in d Hong Ou Mandel effect: only 2 possibilities

Hong, Ou and Mandel PRL 59, 2044 (1987) d c n c = n d 0 n c n d 0 HOM dip as a function of the overlap between the two arms.

2 classical wave packets φ a b d Id c Ic

2 classical wave packets Id 2.0 a d c Ic 1.5 1.0 0.5 IcId φ b 0.0 0.5 1.0 1.5 2.0 0 π φ

2 classical wave packets Id 2.0 a d c Ic 1.5 1.0 0.5 IcId φ b 0.0 0.5 1.0 1.5 2.0 0 π φ correlation function: g (2) Ic Id cd = φ = 1/2 overlapped Ic φ Id φ pulse delay 1 0.5 g (2) cd =1 not overlapped (detector slower than pulse)

2 quantum fields at a beam splitter 1 particle at each input 4 QM amplitudes: d a c b both transmitted both reflected

2 quantum fields at a beam splitter 1 particle at each input 4 QM amplitudes: d a c b both transmitted both reflected G (2) cd = n c n d = 0 two particle interference has no classical analog

Why do it? It s cool... Tests single photon sources Metrology with twin Fock states Santori et al. Indistinguishable photons from a single-photon device Nature, 2002 (one quantum dot) Beugnon et al. Quantum interference between two single photons emitted by independently trapped atoms Nature, 2005

How to do it with atoms Essential features photon coincidence counting source of photon pairs mirrors, beam splitter spatial, spectral filters He*, MCP 4 wave mixing Bragg diffraction MCP

Get a good team Alain Aspect C I W Raphael Lopes Denis Boiron Marc Cheneau Pierre Dussarat Almazbek Imanaliev

Metastable Helium, He* E (ev) Lifetimes: 2 3 S1: 8000 s 2 3 PJ: 100 ns 24.6 20.6 2 1 S0 2 3 P0,1,2 1083 nm 19.8 2 3 S1 deexcitation enables electronic detection: He* He + + e - microchannel plate and delay line anode spatial resolution ~250 µm q.e. > 25% 0 1 1 S0 4 He (no nuclear spin)

Time of flight observation 5 10 4 detectors in // record x,y,t for every detected atom get velocity distribution and correlation functions trap 46 cm detector there is also a laser trap

Pair production: 4 wave mixing in a lattice dynamical instability: 2 k0 k1 + k2 lowest energy band Hillingsoe and Molmer, PRA 2005 Campbell et al. PRL 2006 Bonneau et al. PRA 2013

Bragg diffraction: mirror and beam splitter k1 k2 θ kbragg -1 Angle θ adjusted so that kbragg = k2 - k1 100 µs pulse : mirror 50 µs pulse : 50-50 beam splitter

Experimental sequence a b position z a b time t1 t2 t3 t1 pair creation y z x t2 mirror exchanges ka and kb 45 cm c a c t2-t1 = 500 µs t3 beam splitter b d mixes 2 modes atoms fall to a c detector b d

Filtering Detected atom number 0.00 0.02 0.04 0.06 v z (cm/s) 13.0 11.0 9.0 7.0 a va vb b 6.0 7.0 8.0 v z (cm/s) c 0.12 0.08 0.04 0.00 0.12 0.08 0.04 Detected atom number small slice of the velocity distribution isolates one mode 0.8 atoms/ mode 0.2 detected -2.0 0.0 2.0 v x (cm/s) -2.0 0.0 2.0 v x (cm/s) 0.00

HOM correlation 0.08 G (2) cd = n c n d 0.06 coincidences per shot 0.06 50% contrast G (2) cd 0.04 0.02 observed contrast is mostly due to multiple 0.00 150 300 450 600 750 900 atoms ( s) ~10 hrs of data for each point delay: τ = t3-t2 n.b. t2-t1 = 500 µs Lopes et al. arxiv:1501.03065

Other, non-optical experiments Atoms Kaufmann et al., Science 345, 306 (2014). Electrons Bocquillon et al., Science 339, 1054 (2013). Dubois et al., Nature 502, 659 (2013). Plasmons Fakonas et al., Nature Photonics 8, 317 (2014). Di Martino et al., Phys. Rev. Appl. 1, 034004 (2014) Microwaves Lang et al., Nature Phys, 9, 345 (2013).

2 particle interference in a double well Kaufmann et al., Science 345, 306 (2014)

Future Bell s inequalities without spin degrees of freedom k 1,q 1 + k 2,q 2 Lewis-Swann and Kheruntsyan 1411.0191 Need to increase the repetition rate with low pair production (D. Clément: He* BEC in 7 s) with photons: Rarity and Tapster PRL 1990

Multiparticle interference with spins 2 mode squeezed state in the spin sector B. Lücke, et al «Twin Matter Waves for Interferometry Beyond the Classical Limit», Science, 334, p. 773-776 (2011). Do it in momentum space? Photonic version, Spasibko et al. NJ Phys 2014

Merci Merci

Interference contrast Two obvious causes for G (2) 0: 1. Lack of indistinguishibility i.e. imperfect spatial overlap 2. Occasional presence of more than 1 particle n.b. G (2) aa = a a aa = 0 for the 1,1 state We find Vmax = 0.6 ± 0.1. Data consistent with perfect indistinguishibility but extra particles in the state.

HOM peak? n c 2 2.5 2.0 g (2) cd 1.5 1.0 n c n d 0.5 0.0 200 400 600 800 (µs)

Mean count rates... are roughly constant n c n d 0.24 0.20 0.16 0.24 0.20 0.16 0.08 a b c 0.06 n c. n d 0.04 G (2) cd n c, n d 0.02 0.00 150 300 450 600 750 900 ( s)

Variation of contrast with filter width a b 0.8 V 0.4 0.0 0.2 0.4 0.6 0.8 1.0 0.4 0.5 0.6 0.7 0.8 v z (cm/s) v (cm/s)

Variance in the number difference V = h(n 1 N 2 ) 2 i hn 1 N 2 i 2 hn 1 + N 2 i N1, N2 ~ 100 Vmin ~ 0.75

4 wave mixing in a (moving) optical lattice Energy and quasi-momentum conservation 2k0 = k1+k2 2E0 = E1+E2 Interactions produce a dynamical instability for large k0 Hillingsoe and Molmer, PRA 2005 Campbell et al. PRL 2006 Bonneau et al. PRA 2013

A few characteristics Including mean field Final momenta can be chosen with k0 Turning lattice off stops interaction atom number can be controlled Bonneau et al. PRA 2013

Populations measured beam a P0 = 0.82 P1 = 0.16 P2 = 0.021 beam b P0 = 0.9 P1 = 0.090 P2 = 0.005 we infer n 0.5-0.8 depending on assumptions

A two mode squeezed state

Correlated atom pairs 0.05 krec Correlation function for back to back pairs g (2) (p, p+δp) Jaskula et al. PRL 2010

Microchannel Plate Single atom detection q.e. ~ 25%

Detector photos 8 cm Delay lines MCP + Delay lines

Four wave mixing of free atoms a.k.a. a collision H = â 1 â 2 â 3â 4 + h.c. energy and momentum conservation: k 1 + k 2 = k 3 + k 4 E 1 + E 2 = E 3 + E 4 restricts atoms to a spherical shell Perrin et al. PRL 2007

Detection MCP and delay line hole separation: 24 µm spatial resolution ~250 µm 5 10 4 detectors in // q. e. for He* ~ 25% must be careful about saturation time differences give the position on MCP record x, y, t for each atom reconstruct momentum distribution

! 4 wave mixing, seen in 3D

Other methods why look for alternatives? small occupation per mode (0.1-0.01) not easily controlled relaxation of transverse excitations in BEC Bücker et al. Nat Phys (2011) modulation of speed of sound parametric downconversion of phonons (DCE) Jaskula et al. PRL (2012)

Wave particle duality single photon at a beam splitter (Grangier et al., EPL 1986) If we look for an anticorrelation, we find one n c n d = 0 : If we look for interference, we find it: Wave interpretation Particle interpretation HOM is more subtle because neither interpretation works.

Interference fringes from single photons (Grangier et al., EPL 1986)

Photon pairs A. Migdall, NIST ω 1, k 1 ω 2, k 2 parametric downconversion: 4 wave mixing: H ~ b a1 a2 + h.c. H ~ b1 b2 a1 a2 + h.c. These processes have led to Bell s inequality violations, squeezing, improvements in interferometry...

Hong Ou Mandel effect Start with 1 photon in each input 4 QM amplitudes: both transmitted both reflected 1st two amplitudes cancel, leaving: 2,0 + 0,2 average number in one output port N = 1 variance v = N 2 - N 2 = 1 v = 1/2 without interference normalized variance V = v/v = 2

Laser trap and detector position at detector gives initial velocity