This is a seminar jointly organized by the three groups working on quantum physics and technology at Department of Physics, Kindai University, namely Condensed-Matter Theory (CMT), Quantum Control (QC), and QMB Laboratories.

### Scheduled talks

Fiscal year 2022

Time and Date: 10:45-, December 7, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Kagamihara, Daichi (QMB)

Title: Entanglement entropy in a non-Hermitian linear optical system

Abstract:

Sampling complexity refers to the difficulty of sampling from a distribution close to the desired (e.g., quantum system) probability distribution and is sometimes discussed in the context of quantum supremacy. Recently, by considering the sampling problem of identical bosons time-evolving by a quadratic Hamiltonian from a product state, a transition from the state in which sampling can be done easily to that where it is difficult has been proposed[1]. Furthermore, it has been pointed out that when time evolution is extended to be non-unitary by considering open systems, there is a transition in sampling complexity that has not been observed in unitary systems[2].

The aim of this work is to clarify the relation between the sampling complexity and other complexity measures, such as entanglement entropy. We extend the method to calculate the Rényi entanglement entropy in a unitary non-interacting boson system[3] to the non-Hermitian case. We apply our method to the non-Hermitian situation discussed in Ref. [2] and calculate the Rényi entanglement entropy. We will discuss how the scaling law of the entanglement entropy and sampling complexity are related.

[1] A. Deshpande, B. Fefferman, M. C. Tran, M. Foss-Feig, and A. V. Gorshkov, Physical review letters **121**, 030501 (2018).

[2] K. Mochizuki and R. Hamazaki, arXiv.2207.12624.

[3] D. Kagamihara, R. Kaneko, S. Yamashika, K. Sugiyama, R. Yoshii, S. Tsuchiya, and I. Danshita, arXiv:2207.08353.

Time and Date: 10:45-, December 14, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Kukita, Shingo (QC)

Title: Lower bound on operation time of composite pulses robust against pulse length error

Abstract: Precise control of quantum systems is a cornerstone for realizing high-quality quantum technology such as quantum computing and quantum communication. The performance of control of systems often deteriorates due to systematic errors. In one-qubit control, the pulse length error (PLE) is one of typical systematic errors, which is caused by deviation of the strength of a control field. A composite pulse (CP) is a method for suppressing the effects of such systematic errors. A CP is a sequence of operations, where systematic errors in the operations cancel each other. Many CPs that are robust against the PLE have been found. However, their operation time tends to be longer than a simple one because CPs replace a simple operation with multiple ones. A longer operation time implies stronger decoherence, and thus a shorter CP is preferable from the viewpoint of noise immunity. In this talk, we discuss a lower bound on the operation time of CPs robust against the PLE. This bound is not saturable, but non-trivial.

Time and Date: 10:45-, December 21, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Kunimi, Masaya (Tokyo University of Science)

Title: Proposal for realization of the quantum-spin chain with Dzyaloshinskii-Moriya interaction using Rydberg atom quantum simulators

Abstract: Recently, the combination of optical tweezers and Rydberg atoms has enabled the realization of highly-controllable quantum simulators for quantum spin systems, and various quantum many-body phenomena have been studied. Typical quantum spin models such as the S=1/2 Ising, XY, and XXZ models have been experimentally realized by using Rydberg atoms with optical tweezers [1]. In some actual magnets, the Dzyaloshinskii-Moriya (DM) interaction exists, which originates from spin-orbit couplings. It is well known that the DM interaction causes various nontrivial phenomena. For example, skyrmion [2] and chiral soliton lattice [3] emerge due to the DM interactions. The DM interaction has not been realized in the Rydberg atom quantum simulators.

In this talk, we propose a method to experimentally realize a 1D quantum spin model with the DM interaction using the Rydberg atom systems.

Specifically, a Rydberg state (e.g., |nS>) is coupled to another Rydberg state (|n’S>) by a two-photon Raman transition. The Rabi coupling with different phases at each atom position can be realized by setting the direction of the lasers appropriately. By unitary transformation of this system and transformation to the rotating frame, we can obtain a spin Hamiltonian with the DM interaction.

In addition to the experimental proposal, we will present the numerical results for the DH model [4], whose Hamiltonian has the DM interaction and transverse magnetic field only. We investigate the nonequilibrium dynamics of quantum solitons in the DH model and find that the quantum solitons decay after a long-time evolution. Finally, we also show that the DH model has quantum many-body scar states by explicitly constructing a restricted spectrum generating algebra [5].

[1] A. Browaeys and T. Lahaye, Nature Phys. 16, 132 (2020).

[2] N. Nagaosa and Y. Tokura, Nature Nanotechnology, 8, 899 (2013).

[3] J. Kishine and A. S. Ovchinnikov, Solid State Phys. 66, 1 (2015).

[4] S. Kodama, A. Tanaka, and Y. Kato, arXiv:2209.04227 (2022).

[5] S. Moudgalya, N. Regnault, and B. A. Bernevig, Phys. Rev. B 102, 085140 (2020).

Time and Date: 10:45-, February 8, 2023

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Mikkelsen, Mathias (QMB)

Title: TBA

Abstract: TBA

### Talks in the past

Fiscal year 2022

Time and Date: 10:45-, April 20, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Kokubo, Haruya (CMT)

Title: Dynamics of the wake in the Gross-Pitaevskii model with a small nonlinear coefficient

Abstract: 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).

Time and Date: 10:45-, April 27, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Kagamihara, Daichi (QMB)

Title: Finite temperature phase diagram of a three-dimensional spin-dependent Fermi Hubbard model

Abstract:

Recent experimental developments in ultracold atomic physics enable us to simulate various interesting many-body systems. Combining state-dependent optical lattices [1,2], Feshbach resonances [3], and Rabi coupling between two internal states induced by microwaves or lasers [1,2], one can realize a spin-dependent Fermi Hubbard model (SDFHM) [4].

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).

Time and Date: 10:45-, May 11, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Kukita, Shingo (QC)

Title: Short composite operation robust against two common systematic errors

Abstract: Unavoidable systematic errors hinder precise quantum control. Pulse length error (PLE) and off-resonance one (ORE) are typical systematic errors that are encountered during one-qubit control. A composite operation, one of open-loop error cancellation techniques, can help compensate for the effects of systematic errors during quantum operation. Several composite operations that are robust against either PLE or ORE have been identified. However, few attempts have been made to construct composite operations that are robust against both errors (bi-robust) simultaneously. We develop a new bi-robust composite operation for controlling one-qubit, which exhibits a short operation time [1].

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

Time and Date: 10:45-, May 18, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Kazuta, Hironori (QMB)

Title: Towards quantum simulation of non-ergodic behavior of the one-dimension Bose-Hubbard model with a trapping potential

Abstract:

The recent development of ultracold gas experiments allows us to simulate the thermalization of isolated quantum systems. When the system satisfies the eigenstate thermalization hypothesis (ETH) [1], it thermalizes after long-time evolution. Integrable systems [2] and many-body localized systems (MBL) with random potentials [3] are known as the systems that do not satisfy the ETH. Recently, violation of the ETH has been observed in systems that neither are integrable nor have random potentials [4,5]. Typical examples include quantum many-body scar [4] and stark MBL [5]. In this presentation, I focus on another system that violates the ETH. I specifically investigate the time evolution of the initial state in the one-dimensional ultracold atoms in the trap potential. I will first reproduce the results of a previous study [6] numerically. Then, I will present some preliminary results of our attempts for observing the non-ergodic behavior with the use of a remote quantum simulator developed by the Quantum Optics group at Kyoto University.

[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).

Time and Date: 10:45-, May 25, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Mikkelsen, Mathias (QMB)

Title: Noise correlations and spin-structure factor for the SU(N) Hubbard model

Abstract: The realization of SU(N) Hubbard models experimentally using Alkaline-earth atoms [1] has lead to renewed theoretical interest in this model, see e.g. [2] for a review of the phase diagram. The spin-spin correlations are a natural probe for the SU(N) order in the system and measuring them experimentally is therefore important. It is well-established that the noise correlations measured by time-of-flight experiments, which corresponds to the momentum fluctuations of the initial state, can probe the spin structure factor in the Mott-limit of SU(2)-Hubbard models [3].In this talk I explicitly establish the mathematical relationship between the momentum-momentum fluctuations and spin structure factor for Mott-insulating states in the SU(N)-Hubbard model at any integer filling. The relation is confirmed numerically by DMRG calculations for 1D Fermi-Hubbard models with N=2-6 and it is shown that the momentum fluctuations still reflect the SU(N) order for weaker interactions and incommensurate filling (i.e. in the metallic phases away from the Mott-limit).

[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)

Time and Date: 10:45-, June 1, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Nakamura, Yuki (Kyoto Univ.)

Title: Rydberg atoms described by the Ising model with sign-inverted next-nearest-neighbor interaction

Abstract: In recent years, taking advantages of their high controllability, Rydberg atoms confined in an optical tweezer array have been utilized as a quantum simulator of quantum spin models [1,2]. Controllable quantum simulators using up to 256 neutral atomic arrays have been realized so far, and new quantum phases and related phase transitions have been experimentally observed [2]. In the case of quantum simulators of Ising-type models, the interaction between two spins that has been realized thus far is of van der Waals type, in which the sign of the nearest neighbor interaction is the same as that of the next-nearest neighbor one.

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).

Time and Date: 10:45-, June 8, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Miyai, Seiichiro (QMB)

Title: Towards analysis of correlation propagation velocities in the SU(N) Hubbard model

Abstract: Quantum simulation means mimicking a quantum many-body system of interest by using another system with high controllability. Since its first proposal by Feynman in 1981 [1], quantum simulation has been realized in various experimental systems [2]. One of the most promising applications of quantum simulation is to analyze non-equilibrium dynamics of quantum many-body systems in the sense that it is in general difficult with classical computers [3]. For example, in a quantum simulator consisting of a Bose gas in an optical lattice, the time evolution of equal-time correlation functions has been measured and a mechanism of the correlation propagation based on a quasiparticle picture has been discussed [4]. These quasiparticles are composed of excess particles (doublon) and holes (holon), which can be described as slave-bosons [5].

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).

Time and Date: 10:45-, June 15, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Kiya, Haruki (QC)

Title: General off-resonance-error-robust symmetric composite pulses with three elementary operations

Abstract: The performance of quantum computing is highly dependent on the accuracy of quantum control in each process.Realistic quantum operations suffer from undesirable effects of systematic errors caused by the miscalibration of experimental apparatuses and such errors deteriorate the performance of quantum control.In one-qubit control, one mainly confronts two typical systematic errors: pulse length error (PLE) and off-resonance error (ORE).A composite pulse (CP) is a method used to compensate for such systematic errors.For one-qubit operations, several CPs that are robust against PLE have been found, such as SK1[1], BB1[2] and SCROFULOUS[3].On the other hand, ORE-robust CPs that implement arbitrary \(\theta\)-rotations have been less investigated. The CORPSE family is one of the simplest and most tractable ORE-robust CPs for implementing arbitrary \(\theta\)-ratations[4].

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:

[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]

Time and Date: 10:45-, June 24, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Ichikawa, Tsubasa (QIQB, Osaka University)

Title: Bayenianism, Conditional Probability and Laplace Law of Succession in Quantum Mechanics

Abstract: The axioms of quantum mechanics (QM) assume the existence of a measurer.

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 take 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.

Time and Date: 13:15-, June 30, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Asai, Shiono (Nara Wowen’s Univ.)

Title: Transition between vacuum and finite-density states in the Bose–Hubbard model with spatially inhomogeneous dissipation

Abstract: Recent technological advances in cold-atom experiments enable us to analyze open quantum many-body systems with widely controllable dissipation [1–3]. Previous theoretical studies have considered the dynamics of a Bose–Hubbard system with dissipation processes that tend to lock the phase difference of the particle field between nearest-neighboring sites. It has been shown that steady states reached after long time evolution exhibit a transition between a Bose condensed state and a non-condensed state when the dissipation strength is varied [4,5]. Such transition phenomena in Bose–Hubbard systems with dissipation have recently attracted much attention.

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).

Time and Date: 10:45-, July 6, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Kaneko, Ryui (QMB)

Title: Renyi entropy after a quantum quench starting from insulating states in a free boson system

Abstract: The concept of entanglement is indispensable for understanding quantum many-body physics these days. The entanglement entropy quantifies the degree of entanglement and is a valuable probe for characterizing states of quantum many-body systems. The protocol for measuring the Renyi entropy first proposed in 2012 [1,2] has further stimulated experimental and theoretical research on real-time dynamics of quantum many-body lattice systems. Yet, studies of the entanglement growth during the quench dynamics for (soft-core) bosons are very few, even for a quench to a noninteracting region [3,4].Here we focus on a one-dimensional free boson system and investigate the time-dependent Renyi entanglement entropy after a quantum quench starting from the Mott insulating and charge-density-wave states. We show that the second Renyi entropy is the negative of the logarithm of the permanent of a matrix consisting of time-dependent single-particle correlation functions. We obtain rigorous conditions for satisfying the volume-law entanglement using the permanent inequality [5]. We also successfully calculate the time evolution of the entropy in unprecedentedly large systems by brute-force computations of the permanent. We discuss possible applications of our findings to the real-time dynamics of noninteracting bosonic systems.

[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).

Time and Date: 10:45-, July 22, 2022

Room: Rm. 31-502, 5th Floor, 31 Bldg. + Webcast via Zoom

Speaker: Nagao, Kazuma (RIKEN)

Title: Squeezed coherent state path integral methods for fermions

Abstract: Spontaneous symmetry broken phases, such as Bose-Einstein condensates of dilute bosonic atoms and superconductors of electrons, are ubiquitous and fundamental quantum phases in condensed matter physics, AMO physics, and high-energy physics. In recent years, the Higgs mode of fermionic superconductor/superfluid systems, which is an emergent amplitude excitation mode of the order parameter field, has been extensively explored in many experiments including pump-probe experiments for BCS-type superconductors [1] and a radiofrequency spectroscopy experiment for ultracold two-component Fermi gases [2].

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.

Time and Date: 10:45-, August 2, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Andreas Thomasen (QunaSys)

Title: Contemporary approaches to variational quantum algorithms for quantum chemistry

Abstract: Variational quantum algorithms were initially proposed as enabling the first use-cases of quantum computers, namely determination of ground state properties of molecules, with the variational quantum eigensolver being the most familiar and well-known among them. There are signs that such algorithms have inherent short-comings that in the short term will render them unable to produce useful results on noisy intermediate-scale quantum (NISQ) devices due to noise and even for high-fidelity architectures may not converge due to the occurrence of barren plateaus in the parameter search space. In this seminar we give an overview of these problems and discuss recent approaches to mitigating and potentially overcoming them.

Time and Date: 10:45-, September 28, 2022

Room: Simulation and Experiment Room, 3rd Floor, 31 East Bldg. + Webcast via Zoom

Speaker: Sekino, Yuta (RIKEN)

Title: Optical spin conductivity in ultracold atomic gases

Abstract: In solid-state physics, measurement of optical conductivity, which is conductivity of an alternating electric current obtained in an optical way, plays crucial roles to understand various exotic electron systems such as high-Tc superconductors, non-Fermi liquids, and Dirac electrons [1,2,3]. Similarly, conductivity of an alternating spin current (optical spin conductivity) is expected to be a useful probe to investigate various quantum many-body systems from spin degrees of freedom.

In this presentation, we report our proposal to measure optical spin conductivity of ultracold atomic gases [4]. In this proposal, an alternating spin current is induced by using a time-dependent gradient of magnetic field or the optical Stern-Gerlach effect. The generated current is measured by observing dynamics of spin density profile.

To demonstrate what information the frequency dependence of the spin conductivity can capture, we computed the conductivity of several cold-atomic systems; a spin-1/2 s-wave Fermi superfluid, spin-1 Bose Einstein condensate, Tomonaga-Luttinger liquid, and topological Fermi superfluid [4,5]. In these systems, nontrivial spin excitations result in the frequency dependence of the spin conductivity quite different from that of the conventional Drude conductivity.

References:

[1] C. C. Homes *et al.,* Phys. Rev. Lett. **71**, 1645 (1993).

[2] Y. S. Lee *et al.,* Phys. Rev. B **66**, 041104(R) (2002).

[3] R. R. Nair *et al,* Science **320**, 1308 (2008); K. F. Mak *et al.,* Phys. Rev. Lett. **101**, 196405 (2008).

[4] Y. Sekino, H. Tajima, and S. Uchino, arXiv:2103.02418.

[5] H. Tajima, Y. Sekino, and S. Uchino, Phys. Rev. B **105**, 064508 (2022).