Eliminating cold-collision frequency shifts

Photoionization cross sections of ultracold 88Sr in 1P1 and 3S1 states at 390 nm and the resulting blue-detuned magic wavelength optical lattice clock constraints

We present the measurements of the photoionization cross sections of the excited ¹P₁ and ³S₁ states of ultracold ⁸⁸Sr atoms at 389.889 nm wavelength, which is the magic wavelength of the ¹S₀-³P₀ clock transition. The photoionization cross section of the ¹P₁ state is determined from the measured ionization rates of ⁸⁸Sr in the magneto-optical trap in the ¹P₁ state to be 2.20(50)×10^-20 m², while the photoionization cross section of ⁸⁸Sr in the ³S₁ state is inferred from the photoionization-induced reduction in the number of atoms transferred through the ³S₁ state in an operating optical lattice clock to be 1.38(66) ×10^-18 m². Furthermore, the resulting limitations of employing a blue-detuned magic wavelength optical lattice in strontium optical lattice clocks are evaluated. We estimated photoionization induced loss rates of atoms at 389.889 nm wavelength under typical experimental conditions and made several suggestions on how to mitigate these losses. In particular, the large photoionization induced losses for the ³S₁ state would make the use of the ³S₁ state in the optical cycle in a blue-detuned optical lattice unfeasible and would instead require the less commonly used ³D_1,2 states during the detection part of the optical clock cycle.

Design and operation of a transportable 87Rb atomic fountain clock

A transportable fountain clock with high reliability is important for high-precision time-frequency measurements. Because of its relatively small cold atoms' collision frequency shift and ease of attaining high quantum state preparation efficiency, the rubidium atomic fountain clock has an indicated higher stability and reliability. This paper reports the design and operation of a transportable rubidium atomic fountain clock developed by the Shanghai Institute of Optical and Fine Mechanics, Chinese Academy of Science. After being transported more than 1000 km from Shanghai to the Changping Campus of the National Institute of Metrology, China, the optical platform and other hardware of the fountain clock did not need to be adjusted. The rubidium fountain clock maintained a stability of 4.0 × 10^-13τ^1/2, reaching 5.0 × 10^-16 at 300 000 s. After transportation, the rubidium fountain clock and a cesium fountain clock (NIM5) were operated together against the reference frequency of a hydrogen maser. In three separate operating periods, over a total of nearly three months, the average frequency repeatability of the rubidium fountain was less than 3.8 × 10^-15.

s-Wave collisional frequency shift of a fermion clock

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, θ(1). The fermion shift instead depends strongly on the second pulse area θ(2). It allows the shift to be canceled, nominally at θ(2)=π/2, but correlations perturb the null to slightly larger θ(2). The frequency shift is relevant for optical lattice clocks and increases with the spatial inhomogeneity of the clock excitation field, naturally larger at optical frequencies.

Spin waves and collisional frequency shifts of a trapped-atom clock

We excite spin waves with spatially inhomogeneous Ramsey pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped 87Rb. The density-dependent frequency shifts of the hyperfine transition simulate the s-wave collisional frequency shifts of fermions, including those of optical lattice clocks. As the spin polarizations oscillate in the trap, the frequency shift reverses and it depends on the area of the second Ramsey pulse, exhibiting a predicted beyond mean-field frequency shift. Numerical and analytic models illustrate these observed behaviors.

Optomechanics of a quantum-degenerate Fermi gas

We explore theoretically the optomechanical interaction between a light field and a mechanical mode of ultracold fermionic atoms inside a Fabry-Pérot cavity. The low-lying phonon mode of the fermionic ensemble is a collective density oscillation associated with particle-hole excitations, and is mathematically analogous to the momentum side-mode excitations of a bosonic condensate. The mechanical motion of the fermionic particle-hole system behaves hence as a "moving mirror." We derive an effective system Hamiltonian that has the form of generic optomechanical systems. We also discuss the experimental consequences the optomechanical coupling in optical bistability and in the noise spectrum of the system.

Cancellation of the collisional frequency shift in caesium fountain clocks

We have observed that the collisional frequency shift in primary caesium fountain clocks varies with the clock state population composition and, in particular, is zero for a given fraction of the |F=4,mF=0) atoms, depending on the initial cloud parameters. We present a theoretical model explaining our observations. The possibility of the collisional shift cancellation implies an improvement in the performance of caesium fountain standards and a simplification in their operation.

Cold collision frequency shift in two-dimensional atomic hydrogen

We report a measurement of the cold collision frequency shift in atomic hydrogen gas adsorbed on the surface of superfluid (4)He at T approximately < 90 mK. Using two-photon electron and nuclear magnetic resonance in 4.6 T field we separate the resonance line shifts due to the dipolar and exchange interactions, both proportional to surface density sigma. We find the clock shift Delta nu(c) = -1.0(1) x 10(-7) Hz cm(-2) x sigma, which is about 100 times smaller than the value predicted by the mean field theory and known scattering lengths in the three-dimensional case.

Radio-frequency spectroscopy of ultracold fermions

Radio-frequency techniques were used to study ultracold fermions. We observed the absence of mean-field "clock" shifts, the dominant source of systematic error in current atomic clocks based on bosonic atoms. This absence is a direct consequence of fermionic antisymmetry. Resonance shifts proportional to interaction strengths were observed in a three-level system. However, in the strongly interacting regime, these shifts became very small, reflecting the quantum unitarity limit and many-body effects. This insight into an interacting Fermi gas is relevant for the quest to observe superfluidity in this system.

Pauli blocking of collisions in a quantum degenerate atomic Fermi gas

We have produced an interacting quantum degenerate Fermi gas of atoms composed of two spin states of magnetically trapped 40K. The relative Fermi energies are adjusted by controlling the population in each spin state. Thermodynamic measurements reveal a resulting imbalance in the mean energy per particle between the two species, which is a factor of 1.4 at our lowest temperature. This imbalance of energy comes from a suppression of collisions between atoms in the gas due to the Pauli exclusion principle. Through measurements of the thermal relaxation rate we have directly observed this Pauli blocking as a factor of 2 reduction in the effective collision cross section in the quantum degenerate regime.

Collisional frequency shifts in 133Cs fountain clocks

We present a theoretical analysis of the density dependent frequency shift in Cs fountain clocks using the highly constrained binary collision model described by Leo et al. [Phys. Rev. Lett. 85, 2721 (2000)]. We predict a reversal in the clock shift at temperatures near 0.08 microK. Our results show that s waves dominate the collision process. However, as a consequence of the large scattering lengths in Cs the clock shift is strongly temperature dependent and does not reach a constant Wigner-law value until temperatures are less than 0.1 nK.

Measurement and cancellation of the cold collision frequency shift in an 87Rb fountain clock

We measure a cold collision frequency shift in an 87Rb fountain clock that is fractionally 30 times smaller than that for Cs. The shift is -0.38(8) mHz for a density of 1.0(6)x10(9) cm(-3). We study the cavity pulling of the atomic transition and use it to cancel the cold collision shift. We also measure the partial frequency shifts of each clock state finding 2(lambda(10)-lambda(20))/(lambda(10)+lambda(20)) = 0.1(6).