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# APP TO UNIV WRIT WRIT 1

UCSB

GPA 3.82

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This 18 page Class Notes was uploaded by Miss Jayde Monahan on Thursday October 22, 2015. The Class Notes belongs to WRIT 1 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/226974/writ-1-university-of-california-santa-barbara in Writing at University of California Santa Barbara.

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Date Created: 10/22/15

Crystallization and trimer formation in Fermi mixtures Gora Shlyapnikov LPTMS Orsay France University of Amsterdam Outline Introduction Molecules in Fermi gases Collisional relaxation Molecules in Ferm mixtures Trimer states Crystalline phase and quantum transitions Stability of the crystalline phase bbbbbb Conclusions Collaborations DS Petrov C Salomon ENS GAstrakharchik Barcelona p119 Twocomponent Fermi gases Experiments 40K 6Li Dilute limit an3 ltlt 1 Ultracold limit AT gtgt Re Quantum degeneracy gt JILA 1998 40K At present n N 1013 1014cm3 T N MK JILA LENS nnsbruckMTENSRiceDuke ETH Hamburg Tuebingen Toronto A lt0 Wide resonance gt a BCS I I I I weakly bound Molecules 39 BEC I I p219 Feshbach resonance Bound state of the brown UR at the resonance with continuum of green UR p319 Strongly interacting regime T O kplal gtgt1 gt Only one distance scale 71 13 Only one energy scale EF h2n23m Universal thermodynamis J Ho 0 O 39 o 0 Mean separation between 0 atoms 1413 O o c U Interatomic potential U gt 3body recombination into deep bound states p419 Gas 0f bosonic molecules dimers Region III a gt 0 gt gas of weakly bound bosonic molecules k I Size of a molecule 0 0 I0 na3 ltlt 1 gt weakly interacting Bose gas Weakly bound dimers gt The highest rovibrational state gt Collisional relaxation 739 1ms for Rbg at n N 1013cm 3 p519 Weakly interacting gas of bosonic dimers Elastic interaction BEC stability quotOld answer gt 2a 4body problem Exact solution for a gtgt Re Petrov et al 2003 111 gt 9 variables a 1 Zerorange approximation 1 mr o gt fF2114m 147ra 2 Integral equation for f k gt 0 swave scattering 3 variables R gt oo 11 07 1 07 21 addR 9507 V217Taexp ra add 06a Monte Carlo GiorginiAstracharchik 2004 Diagrammatic approach MKagan et al2005 Gurarie et al2006 p619 Atomdimer collisions Weakly bound dimer N a Size gt Deep bound state w B6 50 A ltlt a 2 NR6 2 particles are identical fermions 1 1 Pauli principle 04ml N keffR 2 N Re 2 p719 Moleculemolecule relaxation collisions 71R R 8 are C e 6 s 255 m CL 739 N gram 1 N seconds Petrov etal2003 Molecules of bosonic atoms Resonant enhancement are ham 739 lt 1ms p819 Suppressed collisional relaxation A 1 0I T a 01 39 o 0 E 39 39 001 2 0001 I I I I I I 3 2 1 0 ABgauss arel 103913 cm3S391 01 40 160 200 3 nm p919 BoseEinstein condensates of molecules Suppressed relaxation Fast elastic collisions add 0611 6mg a g 104 el Efficient evaporalive cooling a BEC JILA Innsbruck MIT ENS Rice v um Molecules in Fermi mixtures Heavy and light fermions 6L140K 6Ll87Sr a gt 0 gt weakly bound molecules km Relaxation into deep bound states What else gt Trimer states M gt m gt BornOppenheimer picture r lt a gt One bound state of a light atom with two fixed heavy ones Mediated attractive potential U R s 4116712 mR2 p1119 Trimer states Pauli principle gt Centrifugal potential UC 2712MR2 U Mediated attraction competes with Pauli principle UeffR U R UCR 016h2mR2 2h2MR2 K KR Mm gt 136 gt fall into center shortrange physics Many nodes of the wavefunction Many trimer bound states p1219 Longrange intermolecular repulsion Molecules of heavy and light fermions BornOppenheimer picture eXp 2Ra U 1M k t P N exp 09 a R M gtgtgt m gt Collisional stability independent of a UR2h 2 maR p1319 Manybody system of molecules No interaction between light fermions BornOppenheimer approach N lowest singleparticle states for a light atom Zerorange approximation for lightheavy interaction Large interheavy distances gt Narrow band of N lightatom states by 60 below the continuum Total energy E N 0 12 Em URz j 60 h2n32m gt molecular binding energy H51 gt molecular size U3DR 4 01 2HOR1 Xp 2 0R 15019 KM HOB ltlt 1 U2DR 460H0RK0lt0RK1lt0R K lt0R KOWR ltlt 1 R m 2lt0 or larger Phase diagram 2D motion of heavy atoms H h22M ARi 12 UR I j Mm gt MmC gt crystalline phase 2D motion of light atoms gt 3D motion of light atoms gt MmC 120 triangular lattice MmC 200 triangular lattice 1000 800 l i 2X3 CRYSTAL 600i 400 f Mm 39 200 EXZ 7 i GAS p1519 Quantum transitions M m gt 0 and n fixed Increase a Cl 1 k gt B t M depends on but always nag ltlt 1 m firstorder transition p1619 Realization of the crystalline phase 3 M m 200 or m 200 gt no gas phase possrble m How to obtain the crystalline phase Optical lattice for heavy fermions Small filling factor gt Increase of Mm Increase of M by a factor of 20 or more is possible MAVMV AVAVAVAVAVAV MAVAVAVAVA MAYNAVAVAVA VVV VVV 7 A Formation of a superlattice p1719 Stability of the crystalline phase Relaxation into deep bound states K A heavy atoms in neighboring sites gt P1 N nL2 exp W jump to one and the same site gt P2 N tU02 t h2ML2 U0 N haul 732Ml2 undergo relaxation process gt 70 1 N hMl1l3 at worst Relaxation rate 7 1 N Pngrgl N nL2MM2lL2hM eXp Mm 739 exceeds 103 even for n N 109cm 2 Formation of trimer states 2 heavy and 1 light atom 4body problem in a lattice gt 739 can range from 01 to 1003 for n N 109 cm 2 p1819

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