Condensation of Excitons in a Trap

Transcription

1 Condensation of Excitons in a Trap I (arb. units) Alex High, Jason Leonard, Mikas Remeika, & Leonid Butov University of California at San Diego Micah Hanson & Art Gossard University of California at Santa Barbara 5 mk K 3 μm T=7 K

2 Traps in Low Temperature Physics Traps are critical for studies of atomic condensates atomic BEC MH Anderson, JR Ensher, MR Matthews, CE Wieman, EA Cornell, Science 269, 98 (995) CC Bradley, CA Sackett, JJ Tollett, RG Hulet, PRL 75, 687 (995) KB Davis, MO Mewes, MR Andrews, NJ van Druten, DS Durfee, DM Kurn, W. Ketterle, PRL 75, 3969 (995) Traps for excitons can be created through customized external potentials goal exciton condensation in a trap

3 An Introduction to Indirect Excitons An indirect exciton is composed of an electron and hole in separate quantum wells Characteristics of indirect excitons long lifetime bosons electronically controllable Model system for studies of physics of ultracold bosons in CM materials QMG.7: Yuliya Kuznetsova Transport of Indirect Excitons in a Potential Energy Gradient Monday, 9:5 AM QM2G.7: Mikas Remeika Electrostatic Lattices for Indirect Excitons in Coupled Quantum Wells Monday, 2:5 PM QThE.: Alex High Spontaneous Coherence in a Cold Exciton Gas Thursday, 5:5 PM

4 Onset of Quantum Degeneracy Quantum gas when thermal de Broglie wavelength comparable to separation between excitons λ db = n -/2 2πħ 2 T db = n mkb 2πħ 2 mk BT () λdb = /2 Excitons in GaAs CQW: n = cm -2, mexciton =.2 m T db ~ 3 K Excitons can cool to mk within lifetime T X Time (ns) L.V. Butov, A.L. Ivanov, A. Imamoglu, P.B. Littlewood, A.A. Shashkin, V.T. Dolgopolov, K.L. Campman, and A.C. Gossard, PRL 86, 568 (2)

5 Exciton Energy (ev) Electronic Control of Excitons Indirect excitons are dipoles with energy controlled by electrode potential V g z x y Customized electrode design creates desired potential landscape δe=ef z d conveyers lattices traps ramps transistors circuits Electrode Voltage V g more info: physics.ucsd.edu/~lvbutov

6 x electrode geometry Vg The Diamond Trap z x Parabolic-like potential along both x- and y-axis y x x 5 simulated potential E (mev ) y (µm) A. A. High, A. K. Thomas, G. Grosso, M. Remeika, A. T. Hammack, A. D. Meyertholen, M. M. Fogler, L. V. Butov, M. Hanson, and A. C. Gossard, PRL 3, 873 (29).

7 Diamond Trap Characterization In situ control r rr to trap center Collection h h h T r-2 ap V oltage-3(v ) -2 T r ap V oltage (V ) T r ap V oltage (V ) energy (mev) Parabolic-like potential (mev T rtap (mev ) )) Tr ap rdepth apdepth Depth (mev 5! m 5! m 5! m y (μm) aa a energy (mev) Trap OFF Trap ON simulated potential x-y emission x-energy emission x (μm) x (μm)

8 Remote Excitation Schematic y (µm) - Excitons are created 6μm from trap center y x e emission µm -5 5 c E (mev) 5 Remote excitation reduces laser heating at the trap center Laser excitation -

9 Emission of Excitons in the Trap I (arb. units) 5 mk K 3 μm T=7 K Sharp peak at trap center emerges with decreasing temperature

10 Coherence Measurements with M-Z interferometer Detector S ample x = µm y (µm) - I 2 I 2 E mis s ion (arb. units) y (µm) - - I I interf Shift interferometry measures the first-order spatial coherence function Iinterf vs. δx g(x)

11 Coherence Measurements: Temperature Dependence a I (arb. units) T bath = 5mK K b I 2 (arb. units).3 Emission (arb. units) c T bath = 5mK 3K 7K d - e µm y 2K 3K K 5K 6K 7K f Interference visibility at shift x = m y (µm) HWHM of exciton cloud (µm) T (K) Excitons condense at the trap bottom Exciton spontaneous coherence emerges with lowering temperature

12 Coherence Measurements: Density Dependence Peak in coherence corresponds to minimum exciton cloud width Interference visibility at shift x = m HWHM of exciton cloud (µm) b c 5 mk.5 K P ex (µw) Non-monotonic dependence on density at 5mK Interference visibility Asymmetry in coherence due to laser heating a shift laser excitation (weak coherence) P ex =.3 µw 2.2 µw 88 µw cold excitons (strong coherence)

13 Coherence Measurements: g(x) vs. T a Interference visibility T bath = 5mK 2K K 8K b (µm) 6 2 I interf at x=7µm T (K) b -2 2 y (µm) 5mK 8K shift Coherence extends over entire cloud at T bath =5mK

14 ξ (µm) ξexperimental vs. T Temperature (K) BEC temperature in a 2-D harmonic trap: Coherence Length vs. T ξ (µm) Estimate of transition temperature Tc = F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 7, 63 (999) corrected for optical spatial resolution ξexperimental ξclassical (λ db / π /2 ) Temperature (K) () g N /2 6 /2 ħω2d ω2d = (ωx ωy) π /2 Trap Frequency: Number of Excitons: ωx ~ 9 s - ωy ~ 3 s - ΔE =.3meV N = 3 T c 2K M. Remeika, J.C. Graves, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 2, 8683 (29)

15 Conclusions Observed condensation of excitons in a trap Excitons condense at the trap bottom Exciton spontaneous coherence emerges with lowering temperature Below a temperature of about K coherence extends over the entire trapped cloud A. A. High, J. R. Leonard, M. Remeika, L. V. Butov, M. Hanson, A. C. Gossard, Condensation of Excitons in a Trap, arxiv:.337, Nano Lett. DOI:.2/nl3983n (7 April 22)