Experimental study of atomic Bose-Einstein condensates with internal degrees of freedom

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1 The 10th US-Japan Joint Seminar Fundamental Issues and Applications of Ultracold Atoms and Molecules Experimental study of atomic Bose-Einstein condensates with internal degrees of freedom Department of Physics, Gakushuin University Takuya Hirano

2 Experimental Quantum Optics Group at Gakushuin Univ. Members 1.0x10 3 Prof. T. Hirano Res. Assoc. S. Tojo (April 2006~) 5.0x10 2 Post. Doc. Yun Zhang (March 2006~) D1 Y. Eto, M2 K. Ishihara, M. Iwata, K. Sirasaki, T. Tajima, T. Furuta M1 S. Tokunaga, A. Furuki B4 R. Okubo, Y. Sanada, M. Tamaki, A. Tomiyama, 5 K. Nagashima, T. Hayashi 3 2 Topics 1 BEC of Rb atoms 0-1 Contineous-variable (CV) quantum information using pulsed light relative phase Quantum cryptography using pulsed homodyne detection Plug & play and free-space implementation at telecommunication. wavelength CV quantum entanglement with pulsed light Pulsed squeezing at telecomm. wavelength カウント 数 noise pow er (db ) 4 ANTISQUEEZED QUADRATURE SQUEEZED QUADRATURE SNL 直 交 位 相 振 幅 entanglement shot noise level

3 Outline 1. Motivation 2. Experimental apparatus 3. Atomic BEC with internal degrees of freedom Dynamical Properties of 87 Rb Spin-2 BEC Optical Confinement of Binary BEC: simultaneous trap of F=1 and F=2 Vortex Formation via magnetic field reversal Thanks to former members: T. Kuwamoto, H. Usuda, K. Hamazaki, Y. Nara 4. Summary

4 Manipulation of Spin States of F=2, 87 Rb BEC in an Optical Trap Motivations Spin degrees of freedom F=2 spinor condensate Is ground state of 87 Rb ferro, anti-ferro, or cyclic states? Mixture of F=1 & F=2 spinor BEC Vortex states in spinor BEC etc Novel Physics in Quantum Fluids with spin Degree of Freedom

5 Experimental setup (1) Double-MOT push beam frequency stabilization repump ECLD (handmade) 20 l/s ion pump 55mW to 1st MOT LD (injection locked) rubidium reservoir valve 1st MOT 150 l/s ion & Ti:subli -mation pump 55mW to 2nd MOT 2mW probe frequency stabilization TC-40 tapered amplifire laser 280mW 2nd MOT glass cell ultra-cold 87 Rb <10 9 pump (MOT to MT) push (1st to 2nd MOT)

6 Atoms in an optical trap 5P 3/2 5P 1/2 5S 1/2 Optical trap 87 Rb BEC D1 D2 Far-off detuned laser D1 : 795 nm D2 : 780 nm 850 nm lens Optical trap potential U 1 = α 2 P Δ E α : polarizability, E :electric field P : laser power Δ : detuning (f laser -f resonace ) Spin degrees of freedom are liberated in an optical trap. First success in Jan

7 Top view OT Beam (radial) Setup of Optical Trap 5 deg. r(radial) g z (axial) λ : 850 nm OT Beam (axial) power fluctuation <1% beam waist radius radial : 90 μm axial : 24 μm coils for magnetic trap Mirror potential depth of OT U ~ 1.0 μk Create BEC in magnetic trap Overlapping Trapping beam 120ms Adiabatic increase in power

8 Lifetime of BEC in Optical Trap - Stretched State (F=2, m F =-2) - N um ber of condenced atom s optical trap Trap tim e (s) magnetic trap with rf shield τ τ loss rate (in the region of N < ) magnetic trap optical trap ~ 7 s ~ 4 s photon scattering rate /s absorption image of the BEC in the optical trap

9 F = 2 state Manipulation of Spin States energy level diagram of 87 Rb ground hyperfine states B=20G m F 2 1 Initial state 0 It is possible to selectively prepare any states MHz -1 Δ=58 khz MHz -2 homogeneous magnetic field optical trap B=20G BEC rf field (Frequency is swept) Parameter of rf field center frequency : MHz sweep range : 80 khz sweep time : 1~3 ms

10 Creation of BEC in m F = 0 state 12 m F = -2 & 0 mixed BEC m F = /11/28 Spatial separation by Stern-Gerlach method gravity gradient magnetic field pulse 30G/cm 1~7ms -2> : 0> = 1:1 m F = We could prepare highly polarized (almost pure) m F =0 BEC. Transfer rate> 90%

11 Decay of F=2, m F =0 BEC in OT at B = 1.5G Time evolution m F = Atoms in BEC initially polarized in F=2, m F =0 state. m F =±1 components appeared during decay process. Total-spin-conserved spin-relaxation process Trap time (ms) N um ber of atom s ( 10 5 ) T rap tim e (m s) m F =0 m F =±1 m F =±2 total 8

12 Magnetic field dependence of spin-mixing dynamics B = 1.5 G B = 0.75 G m F = 0 m F = ±1 m F = ±2 B = 0.3 G B = 0.1 G Oscillation in spin B = 0.75G, 0.3G cf. F=1 Josephson Oscillation: Nature Physics 1, 111 (2005)

13 Relative Populations of Each Component after 70-ms Evolution - Magnetic Field Dependence Kuwamoto et al. Phys. Rev. A 69, (2004). Relative population m F = 0 m F =±1 m F =± M agnetic field (G ) m F = 0 m F = -2 & +2 long time If the F = 2 87 Rb BEC has anti-ferromagnetic properties, the mixture of m F = -2 and m F = +2 is one of the ground states at a zero magnetic field. [ M.Ueda & M.Koashi, PRA, 65, (2002)]

14 Magnetism of F=2 87 Rb BEC If cyclic initial config. m F = -2 & +2 actually m F = -2 & +2 m F = -2 & 0 & +2 m F = -2 & +2 indicates anti-ferromagnetic, but small popuration in m F =±1...

15 Optical Trap of F=1 and F=2 Bose-Einstein Condensates F=1>& F=2> 1> 2> Simultaneous trap of F=1 and F=2 Rb BEC JILA : magnetic trap capable of trapping only weak field seeking states Our experiment : optical trap capable of trapping any states, even for anti-parallel magnetic moment Control of magnetic field

16 Microwave transition Δν~535[kHz] B~255[mG]

17 Experimental setup Microwage GHz ~ 15dBm g z Optcal trap 850nm υ r ~237 Hz υ z ~21 Hz

18 Time evolution for N F=1 N F=2 (without Stern-Gerlach) Trap time 0 ms F=1 & F=2 F=2 only B F=1 & F=2 F=2 only z Field gradient: ~ 30 mg/cm atoms / pixel 1000 F2 F1 B z z 200 ms 400 ms 500 ~100μm ΔB~0.3 mg ΔE~20 nk B z0 B=0 B z B=0 Change bias field 600 ms 300μm g 0 B z0 F1 F2 Force directions are reversed. z TOF 22ms z 180μm

19 Trap time (ms) Center of mass movement of F=2 component Relative center of mass (μm) Change bias field

20 Experimental procedure Initial state Magnetic trap Optical trap 2,-2> 1,-1> Mircowave transition Bias field Micro wave Probe light Change bias field Time ( ms) Evolution time 22

21 Topological Vortex Nucleation in Bose-Einstein Condensates BEC 87 Rb:F=2, m F = 2 c r V s d r h s = m h 8 π = 2 π m 8π 4 B 500mG B z (t ) B (r ) Invert B -500mG t M. Nakahara, et al., Physica (Amsterdam) B, 17(2000). T. Isoshima, et al., Phys. Rev. A 61, (2000). S.-I. Ogawa, et al., Phys. Rev. A 66, (2002). 23 Na (F=1, m F = -1) A. Leanhardt, et al., Phys. Rev. Lett. 89, (2002). 87 Rb (F=2, m F = 2) Kyoto group, Annual meeting JPS, 2004, 27aXG-3 Atomic spin y x ( z >> B r B ) z B total B z B z =, B r B 0 total r total z B B

22 Observation of vortex Experimental procedure 1. Create BEC in a magnetic trap 2. Invert the magnetic field Axial dir. 100μm 3. Absoption imaging gravity # of atoms : TOF : 19ms Inverting time: 5ms Trap time : 5ms Radial dir. Radial-probe Beam Axial-probe Beam 400μm # of atoms : TOF : 15ms Inverting time : 5ms Trap time : 5ms

23 Simultaneous imaging from two directions B 500mG -500mG B z (t ) B (r ) Inverting time Mag. trap OFF Trap Time Imaging t TOF:19ms Invering time:3~13ms 0ms Simultaneous 5ms z (axial) Simultaneous No trapping potential along z axis after inverting the bias field 10ms Individual We cloud observe vortex up to 10ms trap-time TOF : 19ms, Inverting time : 5ms

24 Summary Ground state of 87 Rb Spin-2 BEC For m F =0 initial state, decay at various magnetic field strengths Spin relaxation, population oscillation For m F =±2 initial state, atoms remain in m F =±2 Antiferromagnetic Optical Confinement of Binary BEC: F=1 and F=2 Spatial separation, center of mass movement, domain structure were observed. Vortex Formation via magnetic field reversal Charge 4 vortex, simultaneous imaging from two directions up to 10 msec in magnetic trap, up to ~20 msec in optical trap.