Universal Relations in an Ultracold Fermi Gas

Transcription

1 Universal Relations in an Ultracold Fermi Gas D. Jin JILA, NIST and the University of Colorado $ NSF, NIST

2 Why study atomic gases? Investigate many-body quantum physics with a model system low density, low temperature unique expt tools for probing, manipulating well understood microscopics controllable interactions Fermi superfluid

3 Interactions in an ultracold atom gas T = 50 nk, n = cm -3, T/T F = K spin spin Ultracold atoms interact via a short-range, or contact, interaction.

4 Interactions in an ultracold atom gas Energy r 0 debroglie wavelength ( d, spacing between particles) distance between the atoms Interactions characterized by the s-wave scattering length

5 Interactions in an ultracold atom gas Interactions can be controlled using a Feshbach resonance.

6 The contact and universal relations a breakthrough in our understanding of interacting quantum gases (with short-range interactions) In 2005, two papers by Shina Tan appeared on the arxiv.org preprint server. Energetics of a strongly correlated Fermi gas Large momentum part of a strongly correlated Fermi gas These papers introduced the contact. S. Tan, Annals of Physics 323, 2952 (2008); Ibid., p. 2971; Ibid., p. 2987

7 What is the contact? for Units: length -1 Extensive property of the sy stem Central to exact universal relations, which are independent of details of the interaction applicable to Fermi or Bose gases independent of the state of the system: few-body or many-body T=0 or finite T homogeneous or trapped gas superfluid or normal strong or weak interactions 50/50 or imbalanced spin mixture Theory papers: Tan, Leggett, Braaten, Combescot, Baym, Blume, Werner, Castin, Randeria, Strinati,

8 Tan s universal relations 1. Momentum distribu0on 2. Energy for 3. Local pair density for 4. Adiaba0c sweep theorem 5. Pressure 6. Virial theorem 7. RF lineshape

9 What is the contact? Consider the adiabatic relation C and 1/a are conjugate thermodynamic variables (like P and V, or µ and N) 1/a is the generalized force C is the generalized displacement similar to enthalpy, H=U-PV

10 Measurements of an interacting Fermi gas Other work: Photoassociation (Rice), Partridge et al., Phys. Rev. Lett. 95, (2005) F. Werner, L. Tarruell, and Y. Castin, Euro. Phys. J. B 68, 401 (2009) Bragg spectroscopy (Swinburne) H. Hu et al., arxiv (2009) These experiments extract C and compare to theory, but do not directly test any of the universal relations.

11 Measurements of an interacting Fermi gas 40 K a=0 With 40 K atoms, we can measure momentum distribution of atoms by expanding at a=0.

12 Momentum distribution (normalized) T/T F = 0.11 (in units of k F )

13 Momentum distribution C/k 4

14 Momentum distribution k 4 n(k) (k F a) -1 0 T/T F = 0.11 the Contact (in units of k F ) k

15 Rf spectroscopy (normalized) (in units of E F /ħ)

16 Rf spectroscopy 1/ω 3/2 Γ(ω) ω

17 Rf spectroscopy 2 3/2 π 2 ω 3/2 Γ(ω) (k F a) -1 0 T/T F = 0.11 the Contact (in units of k F ) ω

18 The contact from n(k) and Γ(ω) the contact, C T/T F = 0.11 weak coupling 1/(k F a) strong coupling

19 Comparison with theory the contact, C T/T F = 0.11 weak coupling 1/(k F a) strong coupling T=0 theory line from F. Werner, L. Tarruell, & Y. Castin, Euro. Phys. J. B 68, 401 (2009)

20 Energy measurements kinetic energy interaction energy potential energy E = T + I + V cloud size after expansion (release energy) cloud size in trap ENS, Innsbruck, Duke, JILA

21 Energy Measurements E = T+I+V T/T F = 0.11

22 Adiabatic Sweep Theorem 2π de/d(1/k F a) 1/(k F a)

23 Testing the virial relation (in units of E F ) T+I-V (k F a) -1

24 Conclusion The contact is an important new development in the understanding of interacting gases. We ve measured the contact and directly verified 1. the high-k tail of the momentum distribution 2. the high-ω tail of rf spectroscopy 3. the adiabatic relation 4. the virial relation J. T. Stewart, J. P. Gaebler, T. E. Drake, and D. S. Jin, PRL104, (2010) Future work: use this to probe the physics of strongly interacting gases

25 Thanks.

26 Comparing C with theory Contact T=0 theory line from F. Werner, L. Tarruell, & Y. Castin, Euro. Phys. J. B 68, 401 (2009) (k F a) -1

27 Comparing C with theory Contact (k F a) -1

28 Momentum Distribu0on

29 Momentum-resolved RF Spectroscopy

30 Momentum Distribution With 40 K atoms, we can measure momentum distribution of atoms by expanding at a=0. 1. Suddenly turn off the trap. 2. Suddenly turn off interactions. (fast B ramp to a=0) 3. Let the cloud expand for 6 ms. 4. Take an absorption image: OD(x,y) 5. Take the azimuthal average. 6. Take inverse Abel transform to get n(k). 40 K a=0

31 Energy measurements Release energy 1. Suddenly turn of the trap. 2. Allow the cloud to expand for 16 ms. 3. Take an absorption image: OD(x,z) 4. Find the release energy from the mean squared cloud widths in x and z. Potential energy 1. Suddenly turn of the trap. 2. Allow the cloud to expand for 1.6 ms. 3. Take an absorption image: OD(x, z) 4. Find the potential energy from the mean squared cloud width in z.

32 RF spectroscopy 1. Apply a pulse of rf. 2. Take spin-selective absorption image (at high B). 3. Count how many atoms appear in the new spin state. 4. Vary the rf frequency to obtain an rf spectrum.

33 Turning off the interactions Contact ramp rate (G/µs)