今後の予定

2022年度

In this work, we analyze the dynamics of the infinite-dimensional Bose–Hubbard model with spatially inhomogeneous dissipation by solving the Lindblad master equation with use of the Gutzwiller variational method [6]. We consider dissipation processes that correspond to inelastic light scattering in the case of Bose gases in optical lattices. We assume that the dissipation is applied to half of the lattice sites in a spatially alternating manner. We focus on steady states at which the system arrives after long time evolution. We find that when the average particle density is varied, the steady state exhibits a transition between a state in which the sites without dissipation are vacuum and one containing a finite number of particles at those sites. We also discuss whether this transition can occur also at finite dimensions on the basis of numerical analyses using the cluster mean field approximation.

1 A. Daley, Adv. Phys. 63, 77 (2014).

2 Y. S. Patil, S. Chakram, and M. Vengalattore, Phys. Rev. Lett. 115, 140402 (2015).

3 T. Tomita, S. Nakajima, I. Danshita, Y. Takasu, and Y. Takahashi, Sci. Adv. 3, e1701513 (2017).

4 S. Diehl, A. Tomadin, A. Micheli, R. Fazio, and P. Zoller, Phys. Rev. Lett. 105, 015702 (2010).

5 A. Tomadin, S. Diehl, and P. Zoller, Phys. Rev. A 83, 013611 (2011).

6 S. Asai, S. Goto, and I. Danshita, Prog. Theor. Exp. Phys. 2022, 033I01 (2022).

[1] A. J. Daley et al., Phys. Rev. Lett. 109, 020505 (2012).
[2] D. A. Abanin and E. Demler, Phys. Rev. Lett. 109, 020504 (2012).
[3] M. Cramer et al., Phys. Rev. Lett. 100, 030602 (2008).
[4] A. Flesch et al., Phys. Rev. A 78, 033608 (2008).
[5] R. Berkowitz and P. Devlin, Isr. J. Math. 224, 437 (2018). （編集済み）

In this work, towards establishing a versatile framework to describe those experimental systems, we develop a new path integral representation of fermionic superfluid systems that gives a unified description of the fermionic quasiparticle excitations and the bosonic collective excitations of the order parameter fluctuations. Our approach gives a direct fermionic generalization of the squeezed-coherent-state path integral method for bosons [3]. In this talk, we apply this formalism to BCS superconductors and discuss that a generalized Lagrangian defined for a squeezed fermionic coherent state shows a gapped excitation branch corresponding to the Higgs excitation mode and reproduces the well-known BCS quasiparticle gapped spectrum in a single framework [4]. Additionally, I will also talk about an ongoing project on an application of the method to contact interacting Fermi gas systems [5]. In this work, we analyze the generalized Lagrangian in terms of the momentum-shell renormalization group method and present a new finding on the ground state BCS- BEC crossover phenomenon of the dilute Fermi gas systems.

[1] R. Shimano and N. Tsuji, Annu. Rev. Condens. Matter Phys. 11, 103 (2020).

[2] A. Behrle et al., Nat. Phys. 14, 781 (2018).
[3] I. M. H. Seifie, V. P. Singh, and L. Mathey, Phys. Rev. A 100, 013602 (2019).

[4] K. Nagao, D. Li, and L. Mathey, arXiv:2102.03113.

[5] K. Nagao and L. Mathey, in preparation.

過去の講演

2022年度前期

When an object moves at a constant speed inside a fluid, a wake appears behind the object depending on the size and speed of the object. In a cold atomic gas Bose-Einstein condensate (BEC), quantum vortex generation in the wake of an obstacle has been observed when the velocity of the obstacle potential exceeds the critical velocity [1-2].
The critical velocity is strongly dependent on the shape of the obstacle potential. The critical velocity is about $0.37$ times the speed of sound if the obstacle size is sufficiently larger than the healing length of the superfluid [3-5]. Furthermore, when the obstacle is delta-functional, the critical velocity $v_c$ is near the speed of sound. On the other hand, the critical velocity is zero in the limit that the nonlinear coefficient of the Gross-Pitaevskii equation describing the motion of the cooled atomic gas BEC is zero (linear Schrodinger limit). In this talk,we show that the critical velocity decay with decreasing the nonlinear coefficient and investigate the associated dynamics of the wake and the quantum vortex generation.

[1] G. W. Stagg, N. G. Parker, and C. F. Barenghi, J. Phys. B 47, 095304 (2014).

[2] K. Sasaki, N. Suzuki, and H. Saito, Phys. Rev. Lett. 104, 150404 (2010).

[3] S. Rica, Physica D 148, 221 (2001).

[4] C. T. Pham, C. Nore, and M.E. Brachet, Physica D 210, 203 (2005).

[5] W. J. Kwon, G. Moon, S. W. Seo, and Y. Shin, Phys. Rev. A 91, 053615 (2015).

In this work, we investigate a finite temperature phase diagram of a three-dimensional SDFHM with an attractive interaction. In the ordinary Fermi Hubbard model, the so-called Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein Condensate (BEC) crossover phenomenon is expected. We first review the BCS-BEC crossover based on the Nozières-Schmitt-Rink (NSR) theory [5,6] in the standard Hubbard model. We extend the NSR approach to SDFHM and discuss how differences in hopping amplitudes and Rabi coupling affect the superfluid phase transition temperature.

[1] L. Krinner, M. Stewart, A. Pazmino, J. Kwon, and D. Schneble, Nature 559, 589 (2018).
[2] L. Riegger, Ph.D. Thesis (2019).
[3] C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82 1225 (2010).
[4] W. V. Liu, F. Wilczek, and P. Zoller, Phys. Rev. A 70, 033603 (2004).
[5] P. Nozières and S. Schmitt-Rink, J. Low. Temp. Phys. 59, 195 (1985).
[6] H. Heiselberg, in “The BCS-BEC Crossover and the Unitary Fermi Gas”, edited by W. Zwerger (Springer, New York, 2011).

[1] S. Kukita, H. Kiya, Y. Kondo, arXiv: 2112.12945 [quant-ph]

[1] J. M. Deutsch, Phys. Rev. A 43, 2046 (1991).

[2] T. Kinoshita , T. Wenger & D. S. Weiss, Nature 440 900 (2006).

[3] J. Choi, S.Hild, et al. Science 352, 1547(2016)

[4] C. J. Turner, A. A. Michailidis, et al, Nat. Phys. 14, 745 (2018).

[5] E. van Nieuwenburg, Y. Baum, et al, PNAS 116, 9269 (2019).

[6] M. Kunimi and I. Danshita, Phys. Rev. A 104,043322 (2021).

[1] A.V. Gorshkov et al. Nature Physics 6, 289–295 (2010)
[2] S. Capponi, P. Lecheminant and K. Totsuka, Ann.Phys. 367, 50 (2016)
[3]  E. Altman, E. Demler, and M. D. Lukin, Phys. Rev. A 70, 013603 (2004)

In this talk, I propose a method to realize Ising model with sign-reversed next-nearest neighbor interactions by weakly coupling one Rydberg state to another Rydberg state. I also discuss surface criticality [3,4] as an example of interesting phenomena that can occur in this novel system. I derive Ginzburg-Landau (GL) equation describing the motion of antiferromagnetic order parameters near the first-order phase transition point. By comparing it with numerical calculations of microscopic models in the mean-field approximation, we verify the validity of the analytical calculation based on the derived GL equation for surface criticality.

[1] M. Endres et al., Science 354,6315 (2016).

[2] S. Ebadi et al., Nature 595, 227 (2021).

[3] R. Lipowsky, Phys. Rev. Lett. 49, 1575 (1982).

[4] I. Danshita et al., Phys. Rev. A 91,013630 (2015).

The purpose of this study is to analyze how the propagation velocity of the correlation in the SU (N) Hubbard model behaves by using the slave-boson method. In this presentation, as a preliminary step for this purpose, we review the derivation of the maximum group velocity, which is serves as an estimation of the upper limit of the information propagation velocity in the one-dimensional Bose-Hubbard model, on the basis of the method using auxiliary bosons [5], and the auxiliary bosons method for the Fermi-Hubbard model [6].

[1] R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982).

[2] I. M. Georgescu et al., Rev. Mod. Phys. 86, 153 (2014).

[3] K. Nagao and I. Danshita, Suurikagaku 684, 36 (2020), in Japanese.

[4] M. Cheneau et al., Nature 481, 484 (2012).

[5] P. Barmettler et al., Phys. Rev. A 85, 053625 (2012).

[6] G. Kotliar and A. E. Ruckenstein, Phys. Rev.Lett. 57, 1362 (1986).

In this talk, I explain a systematic construction of a wide class of ORE-robust CPs that implement arbitrary $$\theta$$-rotations.In this class of CPs, we have one continuous free parameter to choose a CP that implements a target operation. We evaluate the performance of the CPs in this class in terms of gate fidelity(and infidelity) and the time required for operation[5].

References:
[1] K. R. Brown, A. W. Harrow, and I. L. Chuang,Phys. Rev. A \textbf{70}, 052318 (2004); K. R. Brown,A. W. Harrow, and I. L. Chuang, Phys. Rev.A \textbf{72}, 039905(E) (2005).
[2] Wimperis, S. 1994 Broadband, narrowband, and passband composite pulses for use in advanced NMR experiments. J. Magn. Reson. A \textbf{109}, 221–231. (doi:10.1006/jmra.1994.1159)
[3] Cummins, H. K. Llewellyn, G. , Jones, J. A. 2003 Tackling systematic errors in quantum logic gates with composite rotations. Phys. Rev. A \textbf{67}, 042308. (doi:10.1103/PhysRevA.67.042308)
[4] H. Cummins and J. Jones, Use of composite rotations to correct systematic errors in nmr quantum computation, New Journal of Physics \textbf{2}, 6 (2000).
[5] S. Kukita, H. Kiya, Y.Kondo, arXiv:2203.05754[quant-ph]

Although this is not a problem in practical terms, it has often been pointed out
by Heisenberg and others that this is a fundamental feature that distincts
QM from classical mechanics.
QBism (Quantum Bayesianism) is a recent attempt of reconstruction of QM
with emphasis on this feature. Here, Bayesianism is the view that probability is
“a measure of one’s degree of belief on whether a given phenomenon will tke place.
QBism follows this view and derives quantum probability (Born rule) as a measure
of the measurer’s degree of belief.
The research question I raise here is whether QBism can derives other relevant
concepts in probability theory such as conditional probability and relative frequency.
The answer is expected to be affirmative, since in Bayesian approach to classical
probability theory, Italian mathematician Bruno de Finetti actually derived these.
In this talk, I would like to brief review of Bruno de Finetti’s work and QBism,
followed by my recent work which derives conditional probability and relative frequency
along the line of the thought of Bruno de Finetti’s works and QBism.

2021年度

2020年度

2019年度