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 2021

Time and Date: 10:45-, December 8, 2021

Room: Webcast via Zoom

Speaker: Sekizawa, Kazuyuki (Tokyo Tech.)

Title: Superfluid Dynamics in Fermionic Systems: From Unitary Fermi Gas to Nuclear Systems

Abstract: Superflulidity is ubiquitous in both Bosonic and Fermionic systems at low temperatures. In Bosonic systems, superfluidity is realized by formation of a Bose-Einstein condensate (BEC) where all particles occupy the lowest energy state. In Fermionic systems, on the other hand, superfluidity is realized through the Cooper pairing mechanism, where two Fermions form a correlated state with an integer total spin, which behaves like a Boson. The most standard scenario (s-wave superfluidity) is realized when all Cooper pairs condense in a zero-momentum state. In the seminar, I will focus on superfluidity in Fermionic systems.Microscopic description of Fermionic superfluids is far more complicated than Bosonic one, since one has to deal with a huge number of quasiparticle wave functions in the system that self-consistently generate superfluidity. Moreover, Fermionic superfluids exhibit various phenomena that are absent in bosonic systems. For instance, one can introduce “spin polarization” to the system, i.e., imbalance of the numbers of spin-up and spin-down particles, which frustrate the Cooper pairing mechanism. As a result, a spontaneous spatial separation of a fully-paired superfluid component from unpaired one was observed experimentally (see, e.g., Refs.[1,2]). A natural question is: how does it affect properties of quantum vortices and their dynamics?

In the seminar, I will give you an answer based on microscopic dynamic simulations employing time-dependent density functional theory (TDDFT) [3] extended for superfluid systems, known as time-dependent superfluid local density approximation (TDSLDA) [4]. Such fully microscopic simulations have become possible only very recently using top-tier supercomputers. Firstly, I will briefly introduce basics of DFT and TDDFT. I will then discuss solitonic excitations and their decays in spin-(un)polarized unitary Fermi gases (UFG) [5]. Our recent attempt [6] to explore quantum turbulence phenomena in rotating UFG is also digested. Finally, as long as time allows, I will discus analogous phenomena in nuclear systems, such as solitonic excitations in collisions of superfluid nuclei [7,8] as well as quantum vortices in neutron stars [9].

[1] M.W. Zwierlein et al., Science 311, 492 (2006).

[2] Y. Shin et al., Phys. Rev. Lett. 97, 030401 (2006).

[3] M.A.L. Marques et al., Fundamentals of Time-Dependent Density Functional Theory, Lecture Notes in Physics , Vol. 837 (Springer, Hidelberg, 2012).

[4] A. Bulgac, P. Magierski, and M.M. Forbes, The unitary Fermi gas: From Monte Carlo to density functionals, in BCS-BEC Crossover and the Unitary Fermi Gas, Lecture Notes in Physics, Vol. 836, pp. 305–373 (Springer, Heidelberg, 2012).

[5] G. Wlazłowski et al., Phys. Rev. Lett. 120, 253002 (2018).

[6] K. Kobuszewski et al., arXiv:2010.07464 [cond-mat.quant-gas].

[7] P. Magierski, K. Sekizawa, and G. Wlazłowski, Phys. Rev. Lett. 119, 042501 (2017).

[8] P. Magierski et al., arXiv:2111.05135 [nucl-th].

[9] G. Wlazłowski et al., Phys. Rev. Lett. 117, 232701 (2016).

Time and Date: 10:45-, December 22, 2021

Room: Rm. 31-302, 3rd Floor, 31st Bldg. + Webcast via Zoom

Speaker: Hakoshima, Hideaki (QIQB, Osaka Univ.)

Title: Relationship between costs for quantum error mitigation and non-Markovian measures

Abstract: Noisy Intermediate-Scale quantum (NISQ) devices are expected to be realized in the near future and have attracted much attention in recent years. Because NISQ devices has difficulty implementing quantum error correction due to the restricted number of qubits and gate operations, they are affected by errors from the environments, such as decoherence, during the calculation process, which prevents them from performing the calculation correctly. Quantum error mitigation (QEM) is known as a method developed to mitigate such errors [1,2]. However, conventional QEM assumes Markovian gate errors, and the non-Markovian case, which appears naturally in many physical systems, has not been studied much. We investigated QEM for non-Markovian errors and evaluated the measurement costs [3]. We found that there is a relationship between the costs of QEM and non-Markovian measures. In this presentation, we will start from the explanation of conventional QEM and the definition of Markovianity, and explain our results based on it.

[1] K. Temme, S. Bravyi, and J. M. Gambetta, Phys. Rev. Lett. 119, 180509 (2017)

[2] S. Endo, S. C. Benjamin, and Y. Li, Physical Review X 8, 031027 (2018)

[3] H. Hakoshima, Y. Matsuzaki, S. Endo, Phys. Rev. A 103.012611 (2021)

Time and Date: 10:45-, February 9, 2021

Room: Rm. 31-302, 3rd Floor, 31st Bldg. + Webcast via Zoom

Speaker: Kaneko, Ryui (QMB)

Title: TBA

Abstract: TBA

### Talks in the past

Fiscal year 2021

Time and Date: 10:45-, April 14, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Kokubo, Haruya (CMT)

Title: Wave pattern formation of quantum Kelvin-Helmholtz instability in binary superfluids

Abstract: Kelvin-Helmholtz instability (KHI) is an instability of an interface in phase separated two component fluids with relative velocity. Sinusoidal growth appears at the interface over time, forming a large spiral structure by this instability [1]. A Weber number is a dimensionless number defined by the ratio of the inertial force of the fluid to the surface tension. This number can characterize the dynamics of interface growth driven by the KHI [2].

An interface in a superfluid causes a phenomenon similar to KHI, and in fact, it has been studied experimentally in a superfluid He [3]. In a Bose-Einstein condensate (BEC) of ultra cold atoms, the dissipation mechanism can be approximately ignored, and thus an instability phenomenon similar to the dynamic instability in the ideal classical fluid can be seen. The KHI in BECs has been studied theoretically [4].

In this talk, we will show that the pattern forming dynamics caused by the KHI can be classified by the Weber number defined for two component superfluids with a relative velocity. This Weber number(We) can be written the ratio an interface thickness to the wave length of the most unstable mode of the KHI in a superfluid. On We << 1, an interface forms finger pattern. On We >> 1, an interface forms either sealskin pattern or zipper pattern depending on the interface thickness.

[1]Hydrokinetic solutions and observations. Kelvin, Load (William Thomson), Phil. Mag. (4), vol.42, 362-377.

[2]Simulation Of Viscous Stabilization Of Kelvin- Helmholtz Instability. AT Dinh, et al., Advances in Fluid Mechanics III

[3]Shear Flow and Kelvin-Helmholtz Instability in Superfluids R. Blaauwgeers, et al. PRL 89, 155301

[4]Quantum Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates Hiromitsu Takeuchi, et al. PRB 81, 094517

Time and Date: 9:00-, April 21, 2021

Room: Webcast via Zoom

Speaker: Iigaya, Kiyohito (California Institute of Technology)

Title: Neural principles of subjective value construction

Abstract: It is an open question how humans construct the subjective value of complex objects (stimuli), such as artistic paintings or photographs. While great progress has been made toward understanding how the brain *adjusts* the value of objects through reinforcement-learning, little is known about how the value *arises* in the brain in the first place. Here, we propose and provide evidence that the brain constructs the value of a novel stimulus by extracting and assembling common features. Notably, because those features are shared across a broad range of stimuli, we show that simple linear regression in the feature space can work as a single neural mechanism to construct the value across stimulus domains. In large-scale behavioral experiments with human participants, we show that a simple model of feature abstraction and linear summation can predict the subjective value of paintings, photographs, as well as shopping items whose values change according to different goals. The model shows a remarkable generalization across stimulus types and participants, e.g. when trained on liking ratings for photographs, the model successfully predicts a completely different set of art painting ratings. Also, we show that these general features emerge through image recognition training in a deep convolutional neural network, without explicit training on the features, suggesting that features relevant for value computation arise through natural experience. Furthermore, using fMRI, we found evidence that the brain actually performs value computation hierarchically by transforming low-level visual features into high-level abstract features which in turn are transformed into valuation. We conclude the feature-based value computation is a general neural principle enabling us to make flexible and reliable value computations for a wide range of complex stimuli.

Time and Date: 10:45-, May 12, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Goto, Shimpei (QMB)

Title: How to make typical(-like) states from product states

Abstract: Recent improvements of imaginary time evolution algorithm in quantum circuits have triggered the development of an algorithm for simulating quantum many-body systems at finite temperatures [1], which has been considered very difficult even in quantum computations. Such an algorithm uses the random sampling of initial product states to evaluate the trace of operators.

In this talk, we show that the trace evaluation based on the random sampling of initial product states could lead to severe inefficiency in 100-qubit scale systems [2]. In order to resolve the sampling inefficiency, we propose two methods: One is effective in classical computers, and the other is designed for fault-tolerant quantum computers.

[1] Shi-Ning Sun *et al*., PRX Quantum 2, 010317 (2021).

[2] Shimpei Goto, Ryui Kaneko, and Ippei Danshita, arXiv:2103.04515.

Time and Date: 10:45-, May 19, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Kukita, Shingo (QC)

Title: Heisenberg-limited quantum metrology by collective dephasing

Abstract: The goal of quantum metrology is the precise estimation of physical parameters using quantum properties such as entanglement. This estimation usually consists of three steps: initial state preparation, time evolution during which information of the parameters is imprinted in the state, and readout of the state. Decoherence during the time evolution typically degrades the performance of quantum metrology and is considered to be one of the major obstacles to realizing entanglement-enhanced sensing. We show, however, that under suitable conditions, this decoherence can be exploited to improve the sensitivity [1]. In this talk, I will introduce a sensing scheme utilizing Markovian collective dephasing. Assume that we have two axes, and our aim is to estimate the relative angle between them. Our results reveal that the use of Markvoian collective dephasing to estimate the relative angle between the two directions affords Heisenberg-limited sensitivity. Moreover, our scheme is robust against environmental noise: it is possible to achieve the Heisenberg limit even under the effect of independent dephasing.

[1]: arXiv:2103.11612 [quant-ph]

Time and Date: 10:45-, May 26, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Kondo, Yasushi (QC)

Title: Quantum Zeno-effect realized in NMR

Abstract: A quantum Zeno-effect is a very counter-intuitive phenomenon and illustrates a difference between classical and quantum measurements: The measurements can be performed without disturbing a system of interest in classical mechanics, while it is not the case in quantum mechanics. We discuss a quantum Zeno-effect experiment realized with a standard high precision NMR spectrometer at Kindai University [1].

[1] Y. Kondo, Y. Matsuzaki, K. Matsushima, and J. G. Filgueiras; New J. Phys. 18, 013033 (2016).

Time and Date: 10:45-, June 2, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Kaneko, Ryui (QMB)

Title: Tensor-network study of quench dynamics of antiferromagnetic correlations in a two-dimensional quantum Ising model

Abstract: Quantum simulators using Rydberg atom arrays have attracted growing interest owing to rapid technological advances [1]. The Rydberg atom arrays can realize the quantum Ising model, which is a fundamental model in statistical physics. Quench dynamics of antiferromagnetic correlations have been observed in the two-dimensional Ising systems [2,3]. Very recently, the number of controllable atoms has exceeded 200 [4,5]. On the other hand, it is also necessary to confirm the validity of the experimental results by numerical simulations on classical computers. To this end, we have applied the tensor-network method [6,7] using projected entangled pair states (PEPS) [8,9], which can handle infinite two-dimensional systems. We have calculated the real-time evolution of antiferromagnetic correlations in the quantum Ising model when the system is quenched from a disordered state. We have found that the estimated phase velocity is maximized locally near the transition point of the ground state phase diagram.

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

[2] E. Guardado-Sanche et al., Phys. Rev. X 8, 021069 (2018).

[3] V. Lienhard et al., Phys. Rev. X 8, 021070 (2018).

[4] S. Ebadi et al., arXiv:2012.12281.

[5] D. Bluvstein et al., Science 371, 1355 (2021).

[6] C. Hubig and J. I. Cirac, SciPost Phys. 6, 031 (2019).

[7] P. Czarnik et al., Phys. Rev. B 99, 035115 (2019).

[8] T. Nishino et al., Prog. Theor. Phys. 105, 409 (2001).

[9] F. Verstraete, J. I. Cirac, arXiv:cond-mat/0407066.

Time and Date: 10:45-, June 9, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Mikkelsen, Mathias (QMB)

Title: Connecting scrambling and work statistics in the interacting harmonic oscillator

Abstract: The non-equilibrium excitations created by sudden changes in the physical parameters of a quantum system (quenches) are well-described by the work probability distribution which establishes a connection to thermodynamics quantities such as the irreversible work [**1**]. The work probability distribution is closely related to the delocalisation of the initial state in the eigenspace of the final Hamiltonian. A different measure of delocalisation, namely the dynamic delocalisation of operators in Hilbert space, known as scrambling, has seen a lot of interest for interacting systems in the last 5 years [**2**]. The scrambling can be quantified by so-called out of-time order correlators (OTOCs). Some specific OTOCs associated with an Ising spin-chain have been measured in an ion setup [**3**]. Such measurements involve a time-reversal of the Hamiltonian, however, and are therefore very difficult for general continuum systems due to the kinetic energy term.In our work [**4**] we investigate interacting particles in a harmonic oscillator after a quench of the trapping frequency, utilizing numeric solutions for up to 5 particles and fully analytic solutions for 2 particles. We show that the scrambling of the single-particle canonical operators is closely related to the work probability distribution, particularly that the infinite-time average of the scrambling is proportional to the work fluctuations. Furthermore we show that our results can be extrapolated to N particles. This further elucidates the role of irreversibility, which is closely related to scrambling, in the quench and links the scrambling to an experimentally accessible quantity, namely the work statistics [**5**] for an important continuum system.

[**1**] M. Á. García-March, T. Fogarty, S. Campbell, T. Busch, and M. Paternostro, *New J. Phys.* **18**, 103035 (2016)

[**2**] B. Swingle, *Nat. Phys. ***14**, 988–990 (2018).

[**3**] M. Gärttner, J. G. Bohnet, A. Safavi-Naini, M. L. Wall, J. J. Bollinger, and A. M.Rey, *Nat. Phys. ***13**, 781–786 (2017).

[**4**] M. Mikkelsen, T. Fogarty and Th. Busch, arXiv:2009.14478 (2020)

*note that this currently only has the 2-particle solution, will be updated soon.

[**5**] M. Cetina, M. Jag, R. S. Lous, I. Fritsche, J. T. M. Walraven, R. Grimm, J. Levinsen, M. M. Parish, R. Schmidt, M. Knap, and E. Demler, *Science*** 354**, 96 (2016)

Time and Date: 10:45-, June 16, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Danshita, Ippei (QMB)

Title: Superfluidity of two-orbital Bose gases in optical lattices

Abstract: Recent experiments have used two-component bosonic atoms in state-dependent optical lattices in order to realize two-orbital Bose gases [1,2]. In this kind of systems, one can induce orbital hybridization by making Rabi coupling between the two internal states of the atom through microwaves [1] or lasers [2]. In this study, we study superfluidity of the two-orbital Bose gases in a situation that one component is delocalized all over the system while the other is localized by a deep optical lattice. We analyze the two-orbital Bose-Hubbard model within the Gross-Pitaevskii mean-field theory and calculate the nonlinear band structure of the energy by using the pseudo-arclength method [3]. We find three different cases with respect to the breakdown of a supercurrent. In one of the cases, when the strength of the orbital hybridization increases, a transition from a superfluid to another superfluid occurs. We discuss how to realize this transition in future experiments.

[1] L. Krinner, M. Stewart, A. Pazmino, J. Kwon, and D. Schneble, Nature **559**, 589 (2018).

[2] L. Riegger, Ph.D. Thesis (2019).

[3] M. Kunimi and Y. Kato, Phys. Rev. A **91**, 053608 (2015).

Time and Date: 10:45-, June 23, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Kagamihara, Daichi (QMB)

Title: BCS-BEC crossover of an ultracold Fermi gas in state-dependent optical lattices

Abstract: Recent experimental developments in ultracold atomic physics enable us to simulate various interesting many-body systems. State-dependent optical lattices make it possible to realize the Hubbard model whose hopping amplitudes depend on atomic internal states [1,2]. Furthermore, one can induce orbital hybridization via Rabi coupling between two internal states by microwaves or lasers [1,2].

In this work, we investigate the superfluid properties of a Fermi gas with attractive interaction in the state-dependent lattices. We consider the so-called Bardeen-Cooper-Schrieffer(BCS)-Bose-Einstein Condensate(BEC) crossover phenomena at absolute zero temperature. We discuss how differences in hopping amplitudes and hybridization affect superfluid properties. We also discuss possibilities of realization of breached-pair (Sarma) phase which is suggested to realize in this system [3].

[1] L. Krinner, M. Stewart, A. Pazmino, J. Kwon, and D. Schneble, Nature **559**, 589 (2018).

[2] L. Riegger, Ph.D. Thesis (2019).

[3] W. V. Liu, F. Wilczek, and P. Zoller, Phys. Rev. A **70**, 033603 (2004).

Time and Date: 10:45-, June 30, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Kasamatsu, Kenichi (CMT)

Title: On truncated Wigner methods for compact U(1) and SU(2) variables

Abstract: The purpose of this study is to explore real time dynamics of quantum systems described by dynamical variables in compact U(1) or SU(2) groups. We employ the truncated Wigner approximation (TWA), which includes quantum correction to the classical mean-field trajectory, demonstrating it by using a few spin-1/2 system. We also show the formulation of TWA with (winding)number-phase representation, which is useful in our problem.

Time and Date: 10:45-, July 7, 2021

Room: Webcast via Zoom

Speaker: Mizuno, Ryota (Kyoto University)

Title: Development of efficient approximation methods in dynamical mean field theory for multi-degree-of-freedom systems

Abstract: Although several impurity solvers in the dynamical mean field theory (DMFT) have been proposed, especially in the multi-degree-of-freedom systems, there are practical difficulties arising from a trade-off between costs and applicability. At least in principle, exact methods, such as the continuous quantum Monte Carlo method (CT-QMC)[2] and the exact diagonalization method (ED) [3], have a broad scope of application. However, especially in multi-degree-of-freedom systems, it is not uncommon that we cannot carry out the calculation practically due to its very high numerical costs. On the contrary, the iterative perturbation theory (IPT) [4-6] has a very low numerical cost, although its scope of application is quite limited.

Given the above, in this study, we provide a new interpretation for IPT from the perspective of the frequency dependence of the two-particle vertices and extended the method such that it can be applied to multi-degree-of-freedom systems [7]. We validated this method by applying it to several models, such as the single-orbital square lattice, the two-orbital square lattice, and the bilayer model, and by comparing it with the numerically exact CT-QMC method. We confirm that our method shows good agreements with CT-QMC. We also propose a simplification of the local two-particle full vertex inspired by the new interpretation of IPT. By using this simplified form of the full vertex, we also develop two low-cost methods to take into account the non-local correlation to DMFT. We apply these methods to the models mentioned above and confirm that our methods can capture important behaviors such as the pseudo-gap. In this talk, we explain the details of the methods and the results.

**Reference**

[1] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg: Rev. Mod. Phys. **68**, 13 (1996).

[2] A. N. Rubtsov, V. V. Savkin, and A. I. Lichtenstein: Phys. Rev. B **72**, 035122 (2005).

[3] M. Caffarel and W. Krauth: Phys. Rev. Lett. **72**, 1545 (1994).

[4] H. Kajueter and G. Kotliar: Phys. Rev. Lett. **77, **131 (1996).

[5] M. S. Laad *et al.*: Phys. Rev. B. **73**, 045109 (2006).

[6] N. Dasari *et al.*:* *The European Physical Journal B. **89**, 202 (2016).

[7] R, Mizuno, M. Ochi, K. Kuroki: arXiv:2101.04466

Time and Date: 10:45-, July 14, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Inoue, Takumi (Cosmology Lab., Kindai Univ.)

Title: Only in Japanese

Abstract: Only in Japanese

Time and Date: 9:00-, July 21, 2021

Room: Webcast via Zoom

Speaker: Güngördü, Utkan (Kyoto University)

Title: Robust implementation of quantum gates despite always-on exchange coupling in silicon quantum dots

Abstract: Single spin qubits in SiMOS quantum dots provide a promising platform for scalable quantum computing, owing to well-developed fabrication techniques and suppressed Overhauser effect due to isotropic enrichment, with gate fidelities ultimately limited by charge noise. Although qubit frequencies and exchange coupling strengths are electrically controllable, there can be severe constraints on the range of tunability and bandwidth, leading to always-on couplings and crosstalk. We consider a double quantum dot device working in this regime with always-on exchange coupling [1], and describe how a controlled-Z (CZ) gate and arbitrary one-qubit gates which are robust against charge noise can be implemented by smoothly pulsing the microwave source while eliminating the crosstalk [2]. We find that the most significant deviations from the rotating wave approximation, which are analogous to the Bloch-Siegert shift in a two-level system, can be compensated using local virtual gates. These results can be extended to a linear chain to three quantum dots [3].

[1] W. Huang, C. H. Yang, K. W. Chan, T. Tanttu, B. Hensen, R. C. C. Leon, M. A. Fogarty, J. C. C. Hwang, F. E. Hudson, K. M. Itoh, A. Morello, A. Laucht, and A. S. Dzurak; Nature (London) 569, 532 (2019)

[2] U. Güngördü, J. P. Kestner; Phys. Rev. B 101, 155301 (2020)

[3] D. W. Kanaar, S. Wolin, U. Güngördü, J. P. Kestner; arXiv:2101.08840 (2021)

Time and Date: 10:45-, July 28, 2021

Room: Rm. 31-808, 8th Floor, 31st Bldg. + Webcast via Zoom

Speaker: Suwa, Mizuki (General Relativity and Cosmology Lab., Kindai Univ.)

Title: Only in Japanese

Abstract: Only in Japanese

Time and Date: 9:00-, October 6, 2021

Room: Rm. 17-402, 4th Floor, 17st Bldg. + Webcast via Zoom

Speaker 1: Kanda, Hiroki (QMB)

Title: Only in Japanese

Abstract: Only in Japanese

Speaker 2: Tanaka, Takayuki (QMB)

Title: Only in Japanese

Abstract: Only in Japanese

Speaker 3: Kiya, Haruki (QC)

Title: Only in Japanese

Abstract: Only in Japanese

Speaker 4: Katayama, Maito (QMB)

Title: Only in Japanese

Abstract: Only in Japanese

Time and Date: 9:00-, October 13, 2021

Room: TBA + Webcast via Zoom

Speaker 1: Nakamura, Yuuki (QMB)

Title: Only in Japanese

Abstract: Only in Japanese

Speaker 2: Miyai, Seiichirou (QMB)

Title: Only in Japanese

Abstract: Only in Japanese

Speaker 3: Kazuta, Hironori (QMB)

Title: Only in Japanese

Abstract: Only in Japanese

Time and Date: 10:45-, October 27, 2021

Room: Rm. 31-302, 3rd Floor, 31st Bldg. + Webcast via Zoom

Speaker: Kokubo, Haruya (CMT)

Title: Critical velocity of quantized vortices generation in small Bose-Einstein condensate

Abstract: When a potential obstacle moves at a speed faster than the critical speed in a cold atomic gas Bose-Einstein condensate (BEC), a quantized vortex is generated in the obstacle’s wake [1-2]. Considering the compressibility of superfluid and the quantum pressure effect near the cylinder boundary, it has been predicted that the critical velocity $v_c$ is similar to $0.37C_s$ when the obstacle is sufficiently large compared to the recovery length of the superfluid [3-5]. $C_s$ is a sound speed. In numerical calculations for BEC with small chemical potential, there were results that a critical velocity is smaller than the expected one [6].

In this study, I investigate the cylindrical companion flow of a small-scale cold atomic gas and its quantum vortex generation by numerical calculations, and evaluate the critical speed in a small-scale BEC. I confirm the dependence of the critical speed on the actual scale of the cold atomic gas.

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

[2]Kazuki Sasaki, Naoya Suzuki, and Hiroki 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]Woo Jin Kwon, Geol Moon, Sang Won Seo, and Y. Shin, Phys. Rev. A **91**, 053615 (2015)

[6]B. Jackson, J. F. McCann, and C. S. Adams, Phys. Rev. Lett. **80**, 3903 (1998)

Time and Date: 10:45-, November 10, 2021

Room: Rm. 31-302, 3rd Floor, 31st Bldg. + Webcast via Zoom

Speaker: Mikkelsen, Mathias (QMB)

Title: Resonant superfluidity in the asymmetric Fermi-Hubbard model with on-site Rabi coupling

Abstract: Progress in cold atomic experiments has enabled the control of interactions and spin-specific tunneling rates in effective Fermi-Hubbard models by exploiting Feshbach resonances and state-dependent optical lattices [1]. In this study we investigate such an asymmetric Fermi-Hubbard model (AFHM) with on-site Rabi coupling between the spin components. In particular we are interested in the limit where one component is almost immobile and superfluidity is suppressed in favor of charge-density-wave order for the Fermion-Fermion pairs that form at attractive interactions [2].

For a symmetric Hubbard model the Rabi coupling is entirely equivalent to a magnetic field for an appropriate rotation of the Hamiltonian which diagonalizes the on-site local Hamiltonian, but for the AFHM a similar rotation results in both an effective magnetic field and an additional tunneling term which transforms between the species. We investigate the model numerically utilizing the DMRG method and derive an effective Hamiltonian for the low-energy sector in the paired phase. We show that superfluidity is resonantly enhanced when the Rabi coupling is slightly smaller than the interaction strength. However, as the Rabi-coupling becomes equal to the interaction strength a transition to a polarized phase takes place as it also contributes to an effective magnetic field. This resonant enhancement allows for superfluidity even when one of the physical components is entirely immobile.

[1] F. Schäfer, T. Fukuhara, S., Sugawa, Y. Takasu, Y. Takahashi* **Nat Rev Phys* **2, **411–425 (2020).

[2] M. A. Cazalilla, A. F. Ho, and T. Giamarchi, *Phys. Rev.Lett.* **95**, 226402 (2005)

Time and Date: 10:45-, November 17, 2021

Room: Rm. 31-302, 3rd Floor, 31st 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-, November 24, 2021

Room: Rm. 31-302, 3rd Floor, 31st Bldg. + Webcast via Zoom

Speaker: Kukita, Shingo (QC)

Title: Geometric Property of Off Resonance Error Robust Composite Pulse

Abstract: The precision of quantum operations is affected by unavoidable systematic errors. A composite pulse (CP), which has been well investigated in nuclear magnetic resonance (NMR), is a technique that suppresses the influence of systematic errors by replacing a single operation with a sequence of operations. In NMR, there are two typical systematic errors, Pulse Length Error (PLE) and Off Resonance Error (ORE). Recently, it was found that PLE robust CPs have a clear geometric property [1] . In this study, we show that ORE robust CPs also have a simple geometric property, which is associated with trajectories on the Bloch sphere of the corresponding operations [2]. We discuss this geometric property of ORE robust CPs using two examples.

[1] Y. Kondo and M. Bando, Journal of the Physical Society of Japan 80, 054002 (2011).

Time and Date: 10:45-, December 1, 2021

Room: Rm. 31-302, 3rd Floor, 31st Bldg. + Webcast via Zoom

Speaker: Ueda, Hiroshi (QIQB, Osaka Univ.)

Title: Development of quantum spin solver QS^{3} and its application

Abstract: Exact diagonalization solvers for quantum spin systems, such as TITPACK [1], KOBEPACK [2], SPINPACK [3] and [4], have been used by many researchers to analyze many-body physics because they allow anyone to easily obtain numerical exact solutions for small numbers of many-body systems. Since these solvers use bit representations for specifying spin states and deal with degrees of freedom that increase exponentially with the system size, they can only perform calculations for quantum spin systems with a few tens of sites. On the other hand, the degrees of freedom for the system in the vicinity of the perfect ferromagnetic state diverge polynomial with the system size, and thus we can perform exact diagonalizations for large-scale quantum spin systems with several hundred to one thousand sites in principle.

We have improved the prototype solver developed for the S=1/2 XXZ model in our previous work [5], and released a simulator for quantum many-body calculations called QS^{3} [6]. The solver can not only obtain eigenstates for quantum spin systems in the vicinity of saturation magnetization, but also numerically exactly perform quantum circuit simulations that satisfy the particle number conservation law starting from such states. In this seminar, the computational principle of the quantum spin solver QS^{3} and the above applications will be explained, and the relevance to the interdisciplinary project of tensor networks and quantum computation that the speaker has been working on recently in JST PRESTO [7] will be introduced.

[1] http://www.stat.phys.titech.ac.jp/~nishimori/titpack2_new/index-e.html

[2] http://quattro.phys.sci.kobe-u.ac.jp/Kobe Pack/Kobe Pack.html

[3] http://www-e.uni-magdeburg.de/jschulen/spin/

[4] M. Kawamura, et al., Comput. Phys. Commun. **217**, 180 (2017).

[5] D. Yamamoto, HU, et al., Phys. Rev. B **96**, 014431 (2017).

[6] HU, S. Yunoki, and Tokuro Shimokawa, arXiv:2107.00872.

[7] https://www.jst.go.jp/kisoken/presto/en/project/1112090/1112090_2019.html