s-Wave Collisional Frequency Shift of a Fermion Clock

Abstract

We report an s-wave collisional frequency shift of an atomic clock based on fermions. In contrast to bosons, the fermion clock shift is insensitive to the population difference of the clock states, set by the first pulse area in Ramsey spectroscopy, θ1. The fermion shift instead depends strongly on the second pulse area θ2. It allows the shift to be canceled, nominally at θ2 = π/2, but correlations shift the null to slightly larger θ2. The shift applies to optical lattice clocks and increases with the spatial inhomogeneity of the clock excitation field, naturally large at optical frequencies. PACS numbers: 06.30.Ft, 34.50.Cx, 37.10.Jk At ultracold temperatures, atom-atom interactions can only occur through s-wave collisions. While s-wave collisions are allowed for bosons and are the most important limitation to the the accuracy of clocks that establish international atomic time [1,2], they are forbidden for identical fermions by the Pauli exclusion principle. Even when dephasing made fermions distinguishable, collision shifts were absent [3]. Thus, ultracold fermions were thought to be immune to swave collisional frequency shifts (sCFS's) making them ideally suited for precision metrology [4][5][6][7][8] and quantum memories [9][10][11][12]. However, recent theoretical work predicted that fermions can have an sCFS because generally occurring inhomogeneities of excitation fields makes particles distinguishable [13][14][15].Here we experimentally observe an s-wave collisional frequency shift of an atomic clock based on a thermal gas of ultracold fermions. Ramsey spectroscopy clearly distinguishes the novel behaviors of the sCFS, via specific dependences on the first and second Ramsey pulse areas, θ 1 and θ 2 . We demonstrate that the shift is insensitive to θ 1 and thereby the difference of the spin populations [13], in stark contrast with the shifts for bosons and the often-used mean-field expression. Instead, the fermion sCFS depends strongly on θ 2 , which reads out the interaction induced phase shifts of each atom. The shift is canceled if the atoms' phases are detected, on average, with equal sensitivity [13]. Interestingly, we show that correlations in the sample perturb the null of the sCFS to θ 2 slightly greater than π/2. We explicitly see that the sCFS increases as expected with the inhomogeneity of the clock field, which we characterize independently. The fermion sCFS we observe in the resolved sideband regime is exactly analogous to those of optical lattice clocks [6], for which the spatial field inhomogeneity is naturally large at optical frequencies. Recently, the fermion sCFS was simulated using an 87 Rb Bose gas [16]. They worked, in contrast, with unresolved trap sidebands to directly excite a spin-wave, and observed the predicted dependence on θ 2 , but an unexpected and unexplained dependence on θ 1 . They elegantly showed a direct link between spin-waves and the fermion sCFS. Here we observe these predicted spin-waves in the resolved sideband regime, demonstrating the dependence of the sCFS ...

Dynamics of Interacting Fermions in Spin-Dependent Potentials

“…Using this formulation, we gain a great deal of insight about the dynamics, and can extract analytic solutions for spin observables and correlations in several limits. Although spin models in energy space [19][20][21][22][23][24][25] have been used before and agreed well with experiments [5,23,[26][27][28][29][30], their use was limited to pure spin dynamics (no motion). Our formulation allows us to track motional degrees of freedom, compute local observables, and determine how correlations spread in real space.…”

Beyond the Spin Model Approximation for Ramsey Spectroscopy

“…A great simplification could be gained if it were possible to decouple the motional and spin degrees of freedom, and reduce the many-body dynamics down to those extracted from a pure interacting spin model. Evidence that this scenario is possible, even far from quantum degeneracy, has been reported in recent experiments [9,13,14,[25][26][27][28], where the observed spin dynamics corresponded to those of a pure spin Hamiltonian. These observations are opening a path for the investigation of quantum magnetism in atomic systems without the need for ultralow temperatures.…”

“…References [21,25] showed that s-wave frequency shifts can be cancelled by setting the second pulse area tō θ n 1 ;n 2 2 ¼ π=2. This result, obtained using the spin model, survives the inclusion of resonant mode changes even for strong interactions during the dark time, since the dependence of the dynamics on the functions f i , and thusθ n 1 ;n 2 2 , remains the same even when interactions are strong.…”

Realizing exactly solvableSU(N)magnets with thermal atoms

“…It is therefore tempting to circumvent the problem of high motional temperature by constructing a spin model in such a way that the motional and spin degrees of freedom are effectively decoupled. We provide a recipe for such a decoupling and hence for realizing spin models with thermal atoms.The first crucial ingredient for implementing such a spin model is to depart from second-order superexchange interactions and use contact interactions to first order [23][24][25][26][27][28][29][30][31][32]. As shown in Fig.…”