Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0907.2245 · Physical Review Letters

Many-Body Treatment of the Collisional Frequency Shift in Fermionic Atoms

Ana María Rey, Alexey Vyacheslavovich Gorshkov, Chester P. Rubbo

Published Dec 22, 2009• 49 citations
arXivHTMLPDF

Abstract

Recent experiments have measured collisional frequency shifts in polarized fermionic alkaline-earth atoms using 1S0-3P0 Rabi spectroscopy. Here, we provide a first-principles nonequilibrium theoretical description of the interaction frequency shifts starting from the microscopic many-body Hamiltonian. Our formalism describes the dependence of the frequency shift on excitation inhomogeneity, interactions, temperature, and many-body dynamics, provides a fundamental understanding of the effects of the measurement process, and explains the observed density shift data.

DOI
10.1103/physrevlett.103.260402

Related papers

Probing Interactions Between Ultracold Fermions

Gretchen K. Campbell, Martin M. Boyd, Jan W. Thomsen +12 more

At ultracold temperatures, the Pauli exclusion principle suppresses collisions between identical fermions. This has motivated the development of atomic clocks with fermionic isotopes. However, by probing an optical clock transition with thousands of lattice-confined, ultracold fermionic strontium atoms, we observed density-dependent collisional frequency shifts. These collision effects were measured systematically and are supported by a theoretical description attributing them to inhomogeneities in the probe excitation process that render the atoms distinguishable. This work also yields insights for zeroing the clock density shift.

arXiv:0902.2558•Science•Apr 16, 2009•121 citations

Probing many-body spin interactions with an optical lattice clock

Ana María Rey, Michael J. Martin, Matthew D. Swallows +6 more

Advances in ultra-stable lasers now permit sub-Hz resolution of optical atomic transitions. At this level, weak interactions by any ordinary scale can in fact dominate the dynamics of the interrogated atoms, even for spin polarized fermions at ultralow temperatures. Contrary to results obtained in radio frequency spectroscopy of alkali fermionic atoms, optical spectroscopy of 87 Sr and 171 Yb has revealed density dependent frequency shifts of the 1 S0 - 3 P 0 “clock” transition. Understanding interactions in these systems is necessary to improve their accuracy and stability. Moreover, such an understanding will enable optical lattice clock systems to serve as quantum simulators for open, driven, strongly-interacting quantum systems at the mesoscopic scale. In this talk we presented our progress towards a comprehensive evaluation and understanding of the interactions present during spectroscopy of the 87 Sr clock transition under various operating conditions. Our studies indicate that a mean-field solution of a master equation is sufficient to capture the many-body dynamics of alkaline earth atom clocks. Entering the regime in which a treatment beyond mean-field is required for a proper description of the clock dynamics is under immediate experimental reach.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•May 1, 2012•1 citation

Evidence of a fermionic collisional shift

W. Maineult, P. Rosenbusch, Christian Deutsch +2 more

We present here experimental result showing that an collisional shift that cannot be explained by mean-field effects. We demonstrate that the latter results from subtle interaction scheme in our cold atomic cloud, mathematically equivalent to a fermionic collisional shift. We show agreement between theory and experiment, and extract the relevant energy scales implied in the collision process.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•May 1, 2011•0 citations

Interacting Ultracold Alkali Atomic Fermion Gases and Radio-Frequency Spectroscopy

Zhenhua Yu

The last chapter focuses on radio-frequency spectroscopy of multi component fermion gases. Rf experiments of 6Li and 40K are first reviewed. We show that rf experiments essentially measure spin correlation functions, and internal symmetries of the interparticle interactions constrain the rf spectrum through sum rules. We self-consistently generate the spin correlation functions for 6Li within Hartree-Fock-BCS approximation. Our calculation reproduces the mean field shift observed in experiments for normal gases, and confirms that a second peak detected at higher frequencies in the rf spectrum at sufficiently low temperatures arises from paired fermions. We define a mean frequency shift by the sum rules, and show that it is proportional to the square of BCS pairing gap. The discrepancy between the mean shift and the peak frequency shift observed in experiment for the condensed phase lies in the broad width of the rf spectrum function.

•Jan 1, 2008•0 citations

Many-body physics of ultracold alkaline-earth atoms with SU(N)-symmetric interactions

Eduardo Ibarra-García-Padilla, Sayan Choudhury

Abstract Symmetries play a crucial role in understanding phases of matter and the transitions between them. Theoretical investigations of quantum models with SU( N ) symmetry have provided important insights into many-body phenomena. However, these models have generally remained a theoretical idealization, since it is very difficult to exactly realize the SU( N ) symmetry in conventional quantum materials for large N . Intriguingly however, in recent years, ultracold alkaline-earth-atom (AEA) quantum simulators have paved the path to realize SU( N )-symmetric many-body models, where N is tunable and can be as large as 10. This symmetry emerges due to the closed shell structure of AEAs, thereby leading to a perfect decoupling of the electronic degrees of freedom from the nuclear spin. In this work, we provide a systematic review of recent theoretical and experimental work on the many-body physics of these systems. We first discuss the thermodynamic properties and collective modes of trapped Fermi gases, highlighting the enhanced interaction effects that appear as N increases. We then discuss the properties of the SU( N ) Fermi–Hubbard model, focusing on some of the major experimental achievements in this area. We conclude with a compendium highlighting some of the significant theoretical progress on SU( N ) lattice models and a discussion of some exciting directions for future research.

arXiv:2408.05359•Journal of Physics Condensed Matter•Nov 22, 2024•17 citations

Radio-frequency spectroscopy of atomic fermi gas

J. J. Kinnunen

This thesis studies radio-frequency spectroscopy of superfluid alkali Fermi gases. Radio-frequency and laser fields provide a coherent and well understood tool for manipulating atomic gases. However, new phenomena are expected and have already been seen experimentally when the alkali atoms become strongly interacting. Here we use a simple perturbative treatment of the atom-rf-field coupling for studying the spectroscopy of a strongly interacting gas. At ultracold temperatures fermionic atoms become paired in analogy to electrons in superconductors. The resulting binding energy, or the pairing gap, can be observed as a shift in the radio-frequency spectrum. With strong interactions, the fermions begin pairing already above the critical superfluid transition temperature. The radio-frequency spectroscopy grants a way to study these fluctuation effects quantitatively. The inhomogeneous trapping potential of the atom cloud also adds its own flavour, resulting in distinct mesoscopic effects in the radio-frequency spectra. Our theoretical models are in very good agreement with the experimental results. First order perturbation theory provides qualitatively correct lineshapes, and our generalised perturbative approach gives quantitatively correct magnitudes for the transfer rates. The inhomogeneity plays an important part also in more exotic systems in which the simple BCS-type pairing of atoms is prevented by polarising the gas. Superfluidity and phase separation in such spin-imbalanced gases has been experimentally observed. We have suggested the use of radio-frequency spectroscopy for observing exotic polarised superfluid states, present at the edges of the atom cloud.

•Jan 1, 2006•0 citations
Recent experiments have measured collisional frequency shifts in polarized fermionic alkaline-earth atoms using 1S0-3P0 Rabi spectroscopy. Here, we provide a first-principles nonequilibrium theoretical description of the interaction frequency shifts starting from the microscopic many-body Hamiltonian. Our formalism describes the dependence of the frequency shift on excitation inhomogeneity, interactions, temperature, and many-body dynamics, provides a fundamental understanding of the effects of the measurement process, and explains the observed density shift data.
At ultracold temperatures, the Pauli exclusion principle suppresses collisions between identical fermions. This has motivated the development of atomic clocks with fermionic isotopes. However, by probing an optical clock transition with thousands of lattice-confined, ultracold fermionic strontium atoms, we observed density-dependent collisional frequency shifts. These collision effects were measured systematically and are supported by a theoretical description attributing them to inhomogeneities in the probe excitation process that render the atoms distinguishable. This work also yields insights for zeroing the clock density shift.
Advances in ultra-stable lasers now permit sub-Hz resolution of optical atomic transitions. At this level, weak interactions by any ordinary scale can in fact dominate the dynamics of the interrogated atoms, even for spin polarized fermions at ultralow temperatures. Contrary to results obtained in radio frequency spectroscopy of alkali fermionic atoms, optical spectroscopy of 87 Sr and 171 Yb has revealed density dependent frequency shifts of the 1 S0 - 3 P 0 “clock” transition. Understanding interactions in these systems is necessary to improve their accuracy and stability. Moreover, such an understanding will enable optical lattice clock systems to serve as quantum simulators for open, driven, strongly-interacting quantum systems at the mesoscopic scale. In this talk we presented our progress towards a comprehensive evaluation and understanding of the interactions present during spectroscopy of the 87 Sr clock transition under various operating conditions. Our studies indicate that a mean-field solution of a master equation is sufficient to capture the many-body dynamics of alkaline earth atom clocks. Entering the regime in which a treatment beyond mean-field is required for a proper description of the clock dynamics is under immediate experimental reach.
The last chapter focuses on radio-frequency spectroscopy of multi component fermion gases. Rf experiments of 6Li and 40K are first reviewed. We show that rf experiments essentially measure spin correlation functions, and internal symmetries of the interparticle interactions constrain the rf spectrum through sum rules. We self-consistently generate the spin correlation functions for 6Li within Hartree-Fock-BCS approximation. Our calculation reproduces the mean field shift observed in experiments for normal gases, and confirms that a second peak detected at higher frequencies in the rf spectrum at sufficiently low temperatures arises from paired fermions. We define a mean frequency shift by the sum rules, and show that it is proportional to the square of BCS pairing gap. The discrepancy between the mean shift and the peak frequency shift observed in experiment for the condensed phase lies in the broad width of the rf spectrum function.
Abstract Symmetries play a crucial role in understanding phases of matter and the transitions between them. Theoretical investigations of quantum models with SU( N ) symmetry have provided important insights into many-body phenomena. However, these models have generally remained a theoretical idealization, since it is very difficult to exactly realize the SU( N ) symmetry in conventional quantum materials for large N . Intriguingly however, in recent years, ultracold alkaline-earth-atom (AEA) quantum simulators have paved the path to realize SU( N )-symmetric many-body models, where N is tunable and can be as large as 10. This symmetry emerges due to the closed shell structure of AEAs, thereby leading to a perfect decoupling of the electronic degrees of freedom from the nuclear spin. In this work, we provide a systematic review of recent theoretical and experimental work on the many-body physics of these systems. We first discuss the thermodynamic properties and collective modes of trapped Fermi gases, highlighting the enhanced interaction effects that appear as N increases. We then discuss the properties of the SU( N ) Fermi–Hubbard model, focusing on some of the major experimental achievements in this area. We conclude with a compendium highlighting some of the significant theoretical progress on SU( N ) lattice models and a discussion of some exciting directions for future research.
This thesis studies radio-frequency spectroscopy of superfluid alkali Fermi gases. Radio-frequency and laser fields provide a coherent and well understood tool for manipulating atomic gases. However, new phenomena are expected and have already been seen experimentally when the alkali atoms become strongly interacting. Here we use a simple perturbative treatment of the atom-rf-field coupling for studying the spectroscopy of a strongly interacting gas. At ultracold temperatures fermionic atoms become paired in analogy to electrons in superconductors. The resulting binding energy, or the pairing gap, can be observed as a shift in the radio-frequency spectrum. With strong interactions, the fermions begin pairing already above the critical superfluid transition temperature. The radio-frequency spectroscopy grants a way to study these fluctuation effects quantitatively. The inhomogeneous trapping potential of the atom cloud also adds its own flavour, resulting in distinct mesoscopic effects in the radio-frequency spectra. Our theoretical models are in very good agreement with the experimental results. First order perturbation theory provides qualitatively correct lineshapes, and our generalised perturbative approach gives quantitatively correct magnitudes for the transfer rates. The inhomogeneity plays an important part also in more exotic systems in which the simple BCS-type pairing of atoms is prevented by polarising the gas. Superfluidity and phase separation in such spin-imbalanced gases has been experimentally observed. We have suggested the use of radio-frequency spectroscopy for observing exotic polarised superfluid states, present at the edges of the atom cloud.