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Quantum Physics

Title: introduction to quantum optics.

Abstract: These are the lecture notes for a course that I am teaching at Zhiyuan College of Shanghai Jiao Tong University (available at this https URL ), though the first draft was created for a previous course I taught at the University of Erlangen-Nuremberg in Germany. It has been designed for students who have only had basic training on quantum mechanics, and hence, the course is suited for people at all levels. The notes are a work in progress, meaning that some proofs and many figures are still missing. However, I've tried my best to write everything in such a way that a reader can follow naturally all arguments and derivations even with these missing bits. Quantum optics treats the interaction between light and matter. We may think of light as the optical part of the electromagnetic spectrum, and matter as atoms. However, modern quantum optics covers a wild variety of systems, including superconducting circuits, confined electrons, excitons in semiconductors, defects in solid state, or the center-of-mass motion of micro-, meso-, and macroscopic systems. Moreover, quantum optics is at the heart of the field of quantum information. The ideas and experiments developed in quantum optics have also allowed us to take a fresh look at many-body problems and even high-energy physics. In addition, quantum optics holds the promise of testing foundational problems in quantum mechanics as well as physics beyond the standard model in table-sized experiments. Quantum optics is therefore a topic that no future researcher in quantum physics should miss.
Comments: Lecture notes and exercise sheets for my quantum optics course, available at
Subjects: Quantum Physics (quant-ph); Optics (physics.optics)
Cite as: [quant-ph]
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Quantum Optics

Topics of study include: the properties of light; fundamentals of quantum mechanics; the interaction of light with photonic crystals, semiconductors, quantum wells and superlattices; ultrafast and nonlinear optical phenomena in condensed matter systems; Bose-Einstein condensation and neutral Fermi gases; trapped ions; plasma physics; and studies of biological systems using optical probes. Such a wide variety of interests are drawn together by a common focus on lasers as primary experimental tools, and on quantum mechanics as the primary theoretical paradigm.

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Nonlinear optics and ultrafast lasers.

Experiment: Robin Marjoribanks ,  Dwayne Miller , Aephraim Steinberg Theory: Daniel James ,  Sajeev John ,  John Sipe

Photonic Materials and Resonant Optical Structures

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Precision Spectroscopy

Experiment: Boris Braverman , Amar Vutha

Quantum Information

Experiment: Boris Braverman, Aephraim Steinberg ,  Hoi-Kwong Lo

Theory: Daniel James ,  Hoi-Kwong Lo ,  John Sipe

Ultra-intense Laser-matter Interaction

Experiment: Robin Marjoribanks

Ultracold Atoms

Experiment: Boris Braverman, Aephraim Steinberg , Joseph Thywissen ,  Amar Vutha

Theory: Sajeev John ,  Daniel James , Hae-Young Kee , Yong Baek Kim ,  Arun Paramekanti ,  John Sipe

See also the research topics listed on the  condensed matter and  biological physics pages, which include QO faculty.

  • Quantum Optics and AMO Physics Seminar series

The QO/AMO (quantum optics and atomic, molecular, and optical physics) seminar is held regularly during the academic year, usually on Fridays at 11:10 am.

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Our Quantum Information seminar is held on Friday mornings at 11:10 am, often in the Fields Institute (222 College St), and is affiliated with the   Centre for Quantum Information and Quantum Control . The QuInf seminar ongoing work and ideas about quantum computation, cryptography, teleportation, et cetera. We hope to bring together interested parties from a variety of different backgrounds, including math, computer science, physics, chemistry, and engineering, to share ideas as well as open questions.

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Our activities are quite interdisciplinary, overlapping with other clusters in the department —  condensed matter and  biophysics — and bridging to other departments, including  chemistry ,  mathematics , and  electrical engineering . Our members participate in two different programs of the Canadian Institute for Advanced Research: Quantum Materials and Quantum Information Processing. Many of the group are founding members of the  Centre for Quantum Information and Quantum Control .

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Quantum Optics Theory

Topics of theoretical research in quantum optics include:

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Quantum optics.

Quantum optics is the study of quantized light (photons) and its interaction with matter. The advancement of quantum optics theory and experiments enabled remarkably precise tests of fundamental questions in physics, as well as applications ranging from lasers to quantum computing. The University of Rochester is one of the world's leading centers of quantum optics since its birth in the 1960's, with the notable distinction of having three former students/faculty, Steven Chu in 1997 and Donna Strickland and Gérard Mourou in 2018, recognized and honored with Nobel Prizes in Physics for their pioneering contributions to quantum optics. In fact, the very term “quantum optics” was coined in Rochester, during the fruitful collaborations of Emil Wolf and Leonard Mandel.

At present there are more than a dozen different research groups at the University involved in different aspects of quantum optics, with a strong interest in foundational questions in quantum mechanics, involving counter-intuitive quantum phenomena such as superposition and entanglement. Simultaneously, our research is driven by the promise of bringing futuristic applications to fruition, including quantum computing, cryptography and teleportation. Research areas include quantum theory (Eberly, Franco, Jordan, Landi), atomic, molecular and optical (AMO) experiments with trapped atoms (Bigelow), defect centers (Vamivakas), nanophotonics (Cardenas, Lin), non-linear optics (Agrawal, Boyd), as well as quantum optics experiments in the solid state with superconducting circuits (Blok), spin qubits (Nichol), 2D materials (Wu) and optomechanics (Renninger). A broad overview of quantum research across all departments of University of Rochester can be found at the UR Quantum website .

Department Research

Departmental research in quantum optics spans a wide range of topics:

  • Professor Agrawal's research interests are in the area of theoretical optics, particularly quantum electronics, nonlinear optics, and laser physics. His current research is focused on nonlinear silicon photonics, highly nonlinear fibers, and all-optical signal processing with semiconductor optical amplifiers.
  • The Cooling and Trapping (CAT) Laboratory of Professor Bigelow is focusing on topological excitations of a spinor Bose-Einstein condensate for fundamental understanding and for application to quantum metrology and information. The CAT group also has a leading program on the formation and control of ultra-cold polar molecules. Experimental and theoretical work spans a range of studies of nonlinear atom (and molecular) optics.
  • Professor Blok’s research focuses on the quantum mechanical properties of superconductors, including superconducting qubits and microwave resonators. Areas of interest include quantum computing with multi-level systems(qudits) and quantum simulation with superconducting circuits.
  • Professor Boyd is interested in studies of the nonlinear interaction of light with matter, in the use of nonlinear optics to control the group velocity of light, in the development of nanostructured materials with exotic optical properties, in the study of quantum states of light, and in the development of applications of these techniques.
  • Professor Cardenas’ research focuses on integrated photonics, nanophotonics, and nonlinear photonics. His group tackles high impact challenges using nanostructured devices on a chip. Current research is focused on four main areas: photonic packaging, 2D materials integrated photonics, nonlinear photonics, and on-chip quantum photonics.
  • Professor Eberly's group is involved in theoretical studies of nonclassical states of radiation, continuous quantum entanglement, optical dark-state solitons, and electron correlation in high-field ionization.
  • Professor Franco works at the interface of chemistry, physics, optics and nanoscience, using theory and simulation to develop new methods to probe and control the behavior of matter by means of external stimuli. Topics of interest include quantum dynamics, investigating basic de-coherence processes in the condensed phase, exploring frontiers of the laser-matter interaction, and advancing single-molecule spectroscopies that can be constructed in the context of nanoscale junctions.
  • Professor Jordan investigates the quantum theory of dynamics and measurement in condensed matter and optical contexts. He is involved in research of electron transport and fluctuations in mesoscopic systems, many-body quantum entanglement, quantum thermodynamics, and the foundations of quantum mechanics.
  • Professor Landi’s research is in the field of theoretical quantum information sciences and technologies. Areas of interest include open quantum systems, quantum thermodynamics, quantum transport and quantum metrology. His recent work focuses on reformulating the laws of thermodynamics, and concepts such as resource expenditure and irreversibility, within a quantum-coherent context.
  • Professor Lin’s research focuses on understanding the fundamental physics of novel nonlinear optical, quantum optical, and optomechanical phenomena in micro-/nanoscopic photonic structures, and on finding their potential applications towards chip-scale photonic signal processing in both classical and quantum regimes.
  • Professor Nichol’s group conducts research on the quantum mechanical properties of individual electrons in semiconductor quantum dots. Particular areas of interest are quantum computing with spin qubits, many-body quantum coherence, and coherent spin-phonon coupling.
  • Professor Renninger’s research interest is in experimental light-matter interactions. His group focuses on ultrafast nonlinear optics and pulsed lasers for applications including imaging deep into the brain. They also investigate the coherent interactions between photons and phonons for applications such as quantum computing, high-speed networking, and dark matter detection.
  • Professor Vamivakas ' research efforts center on light-matter interactions at the nanosclae, using optics to interrogate and control both artificial and naturally occurring solid state quantum emitters. Potential applications range from optical metrology to quantum information science.
  • Professor Wu’s research involves using new quantum materials to create novel electronic devices beyond Moore's law computation. Topics such as spintronics, topological electronics, and multifunctional complex oxide-based transistors are explored from the perspective of materials synthesis, nano-fabrication, and low-noise device characterization.

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A new approach to realize quantum mechanical squeezing

by Ingrid Fadelli , Phys.org

A new approach to realize quantum mechanical squeezing

Mechanical systems are highly suitable for realizing applications such as quantum information processing, quantum sensing and bosonic quantum simulation. The effective use of these systems for these applications, however, relies on the ability to manipulate them in unique ways, specifically by 'squeezing' their states and introducing nonlinear effects in the quantum regime.

A research team at ETH Zurich led by Dr. Matteo Fadel recently introduced a new approach to realize quantum squeezing in a nonlinear mechanical oscillator. This approach, outlined in a paper published in Nature Physics , could have interesting implications for the development of quantum metrology and sensing technologies.

"Initially, our goal was to prepare a mechanical squeezed state, namely a quantum state of motion with reduced quantum fluctuations along one phase-space direction," Fadel told Phys.org. "Such states are important for quantum sensing and quantum simulation applications. They are one of the gates in the universal gate set for quantum computing with continuous-variable systems—meaning mechanical degrees of freedom, electromagnetic fields , etc., as opposed to qubits that are discrete-variable systems."

While performing their experiments and trying to attain an increasing amount of squeezing, Fadel and his colleagues realized that after a certain threshold, the mechanical state was becoming more than merely narrower (i.e., more squeezed) and more elongated. In addition, they found that the state started to twist/twirl around itself, following an "S"-like or even "8"- like pattern.

"We did not expect this, as the preparation of non-gaussian states requires significant nonlinearities in the mechanical oscillator, so we were quite surprised, but of course also excited," Fadel explained.

"Typical mechanical nonlinearities are extremely small and typical couplings between mechanical oscillators and light/microwave fields are also linear. However, it was easy to realize that in our device the resonator was inheriting some of the nonlinearity from the qubit it was coupled to."

The researchers found that the nonlinearities the resonator inherited were quite strong, resulting in the fascinating effect they observed. In their recent paper, they showcased this new approach to realize quantum squeezing in this nonlinear mechanical system.

The system employed in the team's experiments consists of a superconducting qubit coupled to a mechanical resonator via a disk made of a piezoelectric material. The coupling between these two systems results in the effective nonlinearity of the resonator.

"When a two-tone drive is applied to the system at the correct frequencies, f 1 +f 2 =2*f m (where f 1 and f 2 are the two-tone drive frequencies and f m the frequency of the mechanical mode), a parametric process takes place: two microwave photons at frequencies f 1 and f 2 from the drives are converted into a pair of phonons at frequency f m of the mechanics," Fadel said.

"This is very similar to a parametric conversion process in optics, where light fields are sent to a nonlinear crystal that generates squeezing in a similar way as I described."

The new approach for realizing mechanical squeezing introduced by this team of researchers could soon open new opportunities for research and the development of quantum devices. In their experiments, Fadel and his colleagues also used their approach to demonstrate the preparation of non-gaussian states of motion and confirmed that their mechanical resonator exhibits tunable nonlinearity.

"Notably, the nonlinearity we observed in our resonator is tunable, as it depends on the difference between qubit and resonator frequencies, which can be controlled in the experiment," Fadel said.

"The realization of squeezed states has important applications for quantum metrology and for quantum information processing using continuous variables. Non-gaussian states can also be used as a resource for quantum information tasks and for fundamental investigations of quantum mechanics."

In his future studies, Fadel hopes to further investigate the possibility of realizing a mechanical quantum simulator based on the approach introduced in this recent paper. Specifically, this simulator could exploit the possibility of independently addressing and controlling tens of bosonic modes in the team's acoustic resonators.

"Our devices could also find interesting applications in quantum-enhanced sensing of forces, gravitational waves and even tests of fundamental physics," Fadel added. "Recently, we showed in a follow-up work that the mechanical nonlinearity can be so strong that it allows us to realize a mechanical qubit."

Journal information: Nature Physics

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Frequency characteristics of collimated blue light generated by four-wave mixing in cesium vapor

Baodong Yang, Jing Xu, Jian Fan, and Haitao Zhou

Author Affiliations

Baodong Yang, 1, 2, 3, * Jing Xu, 1 Jian Fan, 1 and Haitao Zhou 1, 4

1 College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China

2 State Key Laboratory of Quantum Optics and Quantum Optics Devices and Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China

3 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

4 [email protected]

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  • Nonlinear Optics
  • Diode lasers
  • Four wave mixing
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  • Laser pumping
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  • Original Manuscript: April 12, 2024
  • Revised Manuscript: June 6, 2024
  • Manuscript Accepted: June 6, 2024
  • Published: July 2, 2024
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The frequency evaluation of collimated blue light (CBL) generated by parametric four-wave mixing (FWM) in hot atomic vapor is presented. The cesium ( 133 Cs) atoms are excited from the 6S 1/2 ground state to 8S 1/2 excited state with the 852 and 795 nm pump lasers, producing an optical field at 4.2 µm through an amplified spontaneous emission via population inversion on the 8S 1/2  → 7P 3/2 transition and the 456 nm CBL via FWM on the 7P 3/2  → 6S 1/2 transition. The frequency shift of 456 nm CBL has been measured by velocity-selective optical pumping spectral technique when the frequency of any one of two pumping lasers is tuned. The ratio of the frequency shift of 456 nm CBL to the two-photon frequency detuning of two pumping lasers is 0.8912, implying that the generated 4.2 µm light frequency is also correspondingly shifted.

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Baodong Yang, Jian Fan, Jing Xu, Lanlan Zheng, Wenyi Huang, and Haitao Zhou Opt. Express 32 (3) 3492-3500 (2024)

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X. Zhang, J. B. Kim, and D. Antypas Opt. Lett. 49 (12) 3348-3351 (2024)

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Special Topics in Quantum Optics

  • © 2024
  • Weiping Zhang 0 ,
  • Zeng-Bing Chen 1

Shanghai Jiao Tong University, Shanghai, China

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Nanjing University, Nanjing, China

  • Provides extensive and thorough coverage of quantum optics
  • Presents chapters written by recognized experts in their individual fields
  • Topics covered include cold atoms, cold molecules, quantum control methods and techniques, quantum information, etc

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About this book

This book highlights quantum optics technologies that can revolutionize the way we encode, store, transmit, and handle information. These technologies can help us overcome bottlenecks in classical physics-based information technology in information transmission capacity, computing speed, and information security. The book provides readers with new perspectives on potential applications of the quantum theory. Besides, the book summaries the research advances in quantum optics and atom optics, including manipulation and construction of the quantum states of photons and even atoms, molecules, and matter at the quantum level, and new phenomena and technologies brought about by the interactions between photons and the quantum states of matter.

The book provides extensive and thoroughly exhaustive coverage of quantum optics. It is suitable for researchers and graduate students of optical physics and quantum optics.

Optical Quantum Computing

  • Quantum Optics
  • Atom Optics
  • Optomechanically Induced Transparency
  • Photonic Entanglement
  • Quantum Storage
  • Quantum Teleportation
  • Phase Measurement and Quantum Noise
  • Two-dimensional Magneto-optical Trap
  • Heralded Single-photon Source
  • Quantum Correlation in Raman Scattering
  • Optical Quantum Correlation Interferometer

Table of contents (2 chapters)

Front matter.

Zeng-Bing Chen

New Progress in Quantum Optics and Atom Optics

Weiping Zhang

Back Matter

Editors and affiliations, about the editors.

Wei-Ping Zhang is currently a Zhiyuan Chair Professor at Shanghai Jiao Tong University. He received his Ph.D. degree from Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. His research interests include quantum optics and atom optics, atomic, molecular and optical physics and quantum manipulation and quantum metrology. He is Fellow of Optical Society of America (the U.S.A.) and received the Outstanding Referee Award by American Physical Society (the U.S.A.). He is also granted the honorary titles of National Distinguished Young Scholar (China) and Yangtze River Scholar (China).

Bibliographic Information

Book Title : Special Topics in Quantum Optics

Editors : Weiping Zhang, Zeng-Bing Chen

DOI : https://doi.org/10.1007/978-981-99-8454-1

Publisher : Springer Singapore

eBook Packages : Physics and Astronomy , Physics and Astronomy (R0)

Copyright Information : Shanghai Jiao Tong University Press 2024

Hardcover ISBN : 978-981-99-8453-4 Published: 01 June 2024

Softcover ISBN : 978-981-99-8456-5 Due: 02 July 2024

eBook ISBN : 978-981-99-8454-1 Published: 31 May 2024

Edition Number : 1

Number of Pages : V, 226

Number of Illustrations : 150 b/w illustrations

Topics : Quantum Optics , Quantum Computing , Quantum Physics , Atomic, Molecular, Optical and Plasma Physics

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Sliding ferroelectrics offer fast, fatigue-free switching

Three years ago, researchers from institutions in the US and Israel discovered a new type of ferroelectricity in a material called boron nitride (BN). The team called this new mechanism “slidetronics” because the change in the material’s electrical properties occurs when adjacent atomically-thin layers of the material slide across each other.

Two independent teams have now made further contributions to the slidetronics field. In the first, members of the original US-Israel group fabricated ferroelectric devices from BN that can operate at room temperature and function at gigahertz frequencies. Crucially, they found that the material can endure many “on-off” switching cycles without losing its ferroelectric properties – an important property for a future non-volatile computer memory. Meanwhile, a second team based in China found that a different sliding ferroelectric material, bilayer molybdenum disulphide (MoS 2 ), is also robust against this type of fatigue.

The term “ferroelectricity” refers to a material’s ability to change its electrical properties in response to an applied electric field. It was discovered over a 100 years ago in certain naturally-occurring crystals and is now exploited in a range of technologies, including digital information storage, sensing, optoelectronics and neuromorphic computing.

Being able to switch a material’s electrical polarization over small areas, or domains, is a key part of modern computational technologies that store and retrieve large volumes of information. Indeed, the dimensions of individually polarizable domains (that is, regions with a fixed polarization) within the silicon-based devices commonly used for information storage have fallen sharply in recent years, from roughly 100 nm to mere atoms across. The problem is that as the number of polarization switching cycles increases, an effect known as fatigue occurs in these conventional ferroelectric materials. This fatigue degrades the performance of devices and can even cause them to fail, limiting the technology’s applications.

Alternatives to silicon

To overcome this problem, researchers have been studying the possibility of replacing silicon with two-dimensional materials such as hexagonal boron nitride (h-BN) and transition metal dichalcogenides (TMDs). These materials are made up of stacked layers held together by weak van der Waals interactions, and they can be as little as one atom thick, yet they remain crystalline, with a well-defined lattice and symmetry.

In one of the new works, researchers led by Kenji Yasuda of the School of Applied and Engineering Physics at Cornell University made a ferroelectric field-effect transistor (FeFET) based on sliding ferroelectricity in BN. They did this by sandwiching a monolayer of graphene between top and bottom layers of bulk BN, which behaves like a dielectric rather than a ferroelectric. They then inserted a parallel layer of stacked bilayer BN – the sliding ferroelectric – into this structure.

Yasuda and colleagues measured the endurance of ferroelectric switching in their device by repeatedly applying 100-nanosecond-long 3V pulses for up to 10 4 switching cycles. They then applied another square-shaped pulse with the same duration and a frequency of up to 10 7 Hz and measured the graphene’s resistance to show that the device’s ferroelectricity performance did not degrade. They found that the devices remained robust after more than 10 11  switching cycles.

Immobile charged defects

Meanwhile, a team led by Fucai Liu of the University of Electronic Science and Technology of China , in collaboration with colleagues at Ningbo Institute of Materials Technology and Engineering (NIMTE) of the Chinese Academy of Sciences, Fudan University and Xi Chang University, demonstrated a second fatigue-free ferroelectric system. Their device was based on sliding ferroelectricity in bilayer 3R-MoS 2 and was made by sandwiching this material between two BN layers using a process known as chemical vapour transport. When the researchers applied pulsed voltages of durations between 1 ms and 100 ms to the device, they measured a switching speed of 53 ns. They also found that it retains its ferroelectric properties even after 10 6 switching cycles of different pulse durations.

Based on theoretical calculations, Liu and colleagues showed that the material’s fatigue-free properties stem from immobile charged defects known as sulphur vacancies. In conventional ferroelectrics, these defects can migrate along the direction of the applied electrical field.

atomic layers slide

‘Slidetronics’ makes its debut

Reporting their work in Science , they argue that “it is reasonable to assume that fatigue-free is an intrinsic property of sliding ferroelectricity” and that the effect is an “innovative” solution to the problem of performance degradation in conventional ferroelectrics.

For their part, Yasuda and colleagues, whose work also appears in Science , are now exploring ways of synthesizing their material on a larger, wafer scale for practical applications. “Although we have shown that our device is promising for applications, we have only demonstrated the performance of a single device until now,” Yasuda tells Physics World . “In our current method, it takes many days of work to make just a single device. It is thus of critical importance to develop a scalable synthesis method.”

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  • Published: 03 January 2017

Quantum optics, what next?

  • J. Ignacio Cirac 1 &
  • H. Jeff Kimble 1  

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Quantum optics is a well-established field that spans from fundamental physics to quantum information science. In the coming decade, areas including computation, communication and metrology are all likely to experience scientific and technological advances supported by this far-reaching research field.

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research topics quantum optics

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H. Jeff Kimble is at the Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125, USA, and at JILA, University of Colorado Boulder and the National Institute of Standards and Technology (NIST), USA

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J. Ignacio Cirac is at the Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany,

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research topics quantum optics

BRIEF RESEARCH REPORT article

Shell-model study of weak β-decays relevant to astrophysical processes.

Toshio Suzuki

  • 1 Nihon University, Tokyo, Japan
  • 2 Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki, Japan

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Shell-model studies on the weak β-decay in nuclei relevant to astrophysical processes are carried out. The β-decay rates, as well as electron-capture rates in sd-pf shell induced by Gamow-Teller (GT) transition, are evaluated in astrophysical environments. The weak rates for the nuclear Urca pair of nuclei with A=31 in the island of inversion, which are important for the nuclear Urca processes in neutron star crusts, are investigated by shell-model calculations in the sd-pf shell. The GT strength is evaluated in sd-pf shell for selected β-decays in the sd-shell nuclei, and the effects of the expansion of the configuration space on the quenching of the axial-vector coupling are examined. β-decay rates induced by first-forbidden (FF) transitions are studied by the Behrens-B ühring (BB) method for the isotones with N =126, and compared with the Walecka method. The important role of the electron distortions in the β-decays of 206 Hg and 207 Tl is pointed out.

Keywords: Shell-model, β-decay, weak rates, Gamow-Teller transition, nuclear Urca process, quenching of g A, Forbidden transition

Received: 18 May 2024; Accepted: 08 Jul 2024.

Copyright: © 2024 Suzuki and Shimizu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Toshio Suzuki, Nihon University, Tokyo, Japan

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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