Simulation of neutron-rich dilute nuclear matter using ultracold Fermi gases

Transcription

1 APCTP Focus Program on Quantum Condensation (QC12) Simulation of neutron-rich dilute nuclear matter using ultracold Fermi gases Munekazu Horikoshi Photon Science Center of University of Tokyo Grant-In-Aid for Scientific Research on Innovative Areas Nuclear matter in neutron stars investigating by experiments and astronomical observations Pohang, Korea

2 Neutron stars Treasure box of many-body physics n Neutron matter L n p X Strange-hadron mater? Superfluid!? Superconducting!? Neutron-rich matter Quark matter?? Internal structures and the EOS to sustain the star?

3 Combination of Experiment - Observation - Theory Determination and verification of the EOS Cold Fermi gas Neutron rich nuclei Theories r Astronomical observation unstable nuclei beam factory (RIBF) Strangeness nuclei x-ray satellite ASTRO-H Japan Proton Accelerator Research Complex (J-PARC)

4 Energy Ground experiment : Measurement of the EOS Cold Fermi gas RIBF J-PARC r 0 2r 0 n Neutron matter Neutron rich nuclei Strangeness nuclei

5 Mass of neutron stars M Astronomical observation : Verification of the EOS Mass-Radius curve Balance between gravity and pressure x-ray satellite ASTRO-H (launched in 2014) [ Demorest et al. Nature 467 (2010) 1081 ] Verification of the EOS Radius of neutron stars [km]

6 Condensed matter in neutron stars Superfluidity and pairing gaps are important not only for High-TcSC but also for nuclei Superfluid phase diagram in neutron stars Cooling curve of a neutron star Neutron s-wave superfluid Proton s-wave superconducting Observation Neutron p-wave superfluid [T. Takatsuka and R. Tamagaki, Progress of Theoretical Physics Supplement 112, 27 (1993) ] [PRL 106, (2011)]

7 Mission of our cold atom team Measurement of universal many-body physics and applications Application [ arxiv: ] Equation of state Thermodynamics Density of state Pairing gap s, p-superfluid Transport Universal many-body system Measurements

8 Lenghth scales in cold atom systems particle-specific parameters Scattering amplitude : System-specific parameter

9 Universal many-body system Universal many-body systems independent of details of the particle and the system

10 Universal many-body function and Tan s contact Two-body density matrix at short range : Universal many-body function Tail of the momentum distributions of particles : [Zhang and Leggett, PRA 79, (2009)] Physics 3, 48 (2010) Tan s contact [S. Tan, Ann. Phys. 323, 2952 (2008)]

11 Universal equation of state (EOS) for a dilute Fermi system Adiabatic relation : Total differential of the internal energy : Grand canonical potential : New thermodynamic variable Total differential of the grand canonical potential : EOS of the universal many-body system :

12 BCS-BEC crossover in cold atom systems Fermi liquid Thermal molecule BCS limit BEC limit BCS superfluid Molecular BEC Unitarity limit [N. Navon, et al., Science 328, 729 (2010) ] [ M. Horikoshi, et al., Science 327, 442 (2010) ] [ S. Nascimbène, et al., Nature 463, 1057 (2010) ] [ M. Ku, et al., Science 335, 563 (2012) ]

13 Cold Fermi gases and the inner crust of neutron stars Neutron-rich dilute region (from unitarity to BCS regime) Fermi liquid Thermal molecule BCS limit BCS superfluid Molecular BEC BEC limit Unitarity limit

14 Mission of our cold atom team Measurement of universal many-body physics and applications Application [ arxiv: ] Equation of state Thermodynamics Density of state Pairing gap s, p-superfluid Transport Universal many-body system Measurements

15 Our Photon Science Center of University of Tokyo 2D MOT Since April, 2011 Li oven 3D MOT Prof. Gonokami Graduate studentt : Togashi Undergraduate student : Ito Simultaneous MOT of 6 Li and 7 Li

16 The most serious problem is inhomogeneity of the gas trapped in a harmonic trap T, a, n(r), P(r), μ(r), q (r), x(r) U trap (r) Thermodynamic quantities are position dependent Measured momentum distributions are averaged values over the trap Thermometer, Pressure meter, Chemical potential meter?

17 Our previous route to determine the EOS at the unitarity limit [ M. Horikoshi, et al., Science 327, 442 (2010) ] Force balance : Pressure energy relation : Internal energy : Thermodynamic relationship EOS at the unitarity :

18 Improved our data Recently, thermometry provided by J. Thomas s group has been improved, especially, at high T/T F region. [arxiv: ] Internal energy EOS at unitarity

19 Our previous route to determine the EOS at the unitarity limit [ M. Horikoshi, et al., Science 327, 442 (2010) ] Force balance : Pressure energy relation : Internal energy density : Thermodynamic relationship EOS at the unitarity : unknown

20 ENS s route to determine the EOS at the unitarity limit EOS at the unitarity : [S. Nascimbène, et al., Nature 463, 1057 (2010) ] Pressure : Temperature : direct measurement by mixing 7 Li into 6 Li Chemical potential : Fitting

21 ENS s route to determine the EOS at the unitarity limit EOS at the unitarity : [S. Nascimbène, et al., Nature 463, 1057 (2010) ] Pressure : Temperature : direct measurement by mixing 7 Li into 6 Li Chemical potential : [Tin-Lun Ho and Erich J. Mueller, Phys. Rev. Lett. 92, (2004)]

22 Derivation of the internal energy EOS via ENS s route : P(μ, T, a= ) Particle density:n=(dp/dμ) T,a Entropy density:s = (dp/dt) μ,a

23 Verification of the measured EOS Fermi liquid Thermal molecule BCS limit BCS superfluid Molecular BEC BEC limit Unitarity limit

24 Correction of the effective range of neutrons Correction non-negligible value Adiabatic relation for an effective range : [arxiv: ] Effect of protons is another issue Theoretical support is necessary

25 Summary Simulation of neutron-rich dilute nuclear matter using ultracold Fermi gases Cold Fermi gas Inner crust of neutron stars Correction of the effective range Protons Theories