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An atomic physicist who compiles detailed reference data for alkali chemical atoms, including rubidium-87. His tables and derivations connect measured transition frequencies, hyperfine structure, Zeeman shifts and transition strengths to calculations used in laser cooling and precision spectroscopy. For example, the Breit-Rabi formula and the rubidium-87 clock transition data let an experimenter estimate how a residual magnetic field shifts a frequency reference.^[ref]

An experimental physicist who coauthored a 2000 study of quantum vortex formation in a stirred rubidium-87 Bose-Einstein condensate. A focused laser beam stirred the gas inside a magnetic trap. Above a threshold rotation frequency, vortices appeared; faster stirring produced multiple vortices. Measuring the single-vortex lifetime after stirring stopped made rotational excitations a controlled probe of a dilute quantum fluid.^[ref]

Two complementary signatures are suppressed low-speed dissipation and quantized circulation. Condensation alone establishes macroscopic occupation, not all of these flow properties. In a uniform weakly interacting condensate, the Landau criterion givesfor the Bogoliubov spectrum. Creating an excitation in a flow changes energy by $E(\mathbf{p})-\mathbf{v}\cdot \mathbf{p}$; a negative value allows energy transfer. Boundaries and vortex nucleation can make an actual measured threshold lower than this ideal bulk sound speed.

In the moving-obstacle test of atomic superfluidity, a blue-detuned focused laser repelled atoms in a sodium condensate and was scanned at different speeds. After a fixed exposure, time-of-flight absorption imaging measured the reduction of condensate fraction as a heating indicator. Low-speed heating was small, with a pronounced onset near $1.6mm/s$, below the peak-density sound speed near $6.2mm/s$. A stationary-beam control showed no heating; above-transition clouds constrained heating through the noncondensed fraction. Changing scan frequency and amplitude at common obstacle velocity helped separate a flow threshold from a particular trap resonance. Density inhomogeneity, obstacle geometry and vortex nucleation limit identification of the observed onset with a unique homogeneous Landau velocity.^[ref]

A second experiment stirred rubidium-87 in a magnetic trap by rotating a small transverse anisotropy generated with a far-detuned attractive laser. After stirring, the cloud expanded for $27\mathrm{ms}$ and absorption imaging along the rotation axis revealed vortex cores. Below a threshold no cores appeared; faster rotation produced one or several. Ramping the stirrer down before release reduced additional excitation, and waiting after removing it tested vortex survival. Beam-centre stability and residual trap anisotropy are important controls; an isolated density dip without the rotation and persistence evidence would be less conclusive. This stirred-condensate vortex experiment is a response to rotation, distinct from merely imaging the appearance of a condensate.^[ref]

The superfluid velocity is ${\mathbf{v}}_s=(\hslash /m)\nabla \theta$. A closed loop avoiding a core must return a single-valued order parameter, soA singly quantized vortex therefore has $2\pi$ phase winding and circulation $h/m$, with depleted density in a core of order the healing length. This quantized rotational response differs from ordinary rigid-body flow. The experiment supports that interpretation through controlled stirring and vortex formation; imaging cores alone does not independently measure every phase winding or an absolute zero dissipative rate.

A good atomic qubit needs two reproducible, orthogonal internal states whose populations and relative quantum phase survive for many gate times. Both should be long lived, with weak spontaneous emission and little decoherence from fluctuating fields or atomic motion. Their transition must nevertheless permit fast, selective, coherent control with little leakage to other states. Reliable initialization and state-selective quantum measurement are also required; optical pumping and fluorescence readout can supply these functions.

For rubidium-87, use the two ground state hyperfine levels in the $5{}^2{S}_{1/2}$ electronic configuration. The electronic angular momentum is $J=1/2$, and addition of angular momentum to the given nuclear spin $I=3/2$ gives $F=|I-J|,\dots ,I+J=1,2$. A suitable Rubidium-87 clock qubit isThese are coupled electron-nucleus angular momentum eigenstates, rather than two bare nuclear-spin projections. Their hyperfine structure supplies a resolvable splitting ${\nu }_{01}\simeq 6.835\mathrm{GHz}$. Both belong to the electronic ground state, avoiding a short optical excited-state lifetime. Since the weak-field Zeeman shift is proportional to $g_F{m}_{F}B$, both have zero linear shift at $B=0$: their rubidium-87 clock transition suppresses first-order magnetic-field dephasing near zero field. A quadratic Zeeman shift of a clock transition and differential optical shifts remain. A small stable bias field can define the quantization axis and help resolve unwanted transitions, at the cost of some residual magnetic sensitivity.^[ref]

Drive the magnetic dipole transition with a resonant microwave field of suitable polarization, here $\Delta m_F=0$, or use two phase-coherent optical fields for a far-detuned stimulated Raman transition with their frequency difference resonant with ${\nu }_{01}$. The optical excited state is then only virtually populated, reducing spontaneous emission. In the rotating frame and rotating-wave approximation, define the drive phase $\varphi$ by the effective HamiltonianHere $X,Y,Z$ are the Pauli matrices on the chosen qubit, and $\Omega$ is the Rabi angular frequency. Pulse duration controls the rotation gate angle, while phase selects the axis in the equatorial plane of the Bloch sphere. A $\pi$ pulse exchanges the populations; a $\pi /2$ pulse makes an equal quantum superposition from either basis state. Controlled Rabi detuning, a differential energy shift, or compositions of these pulses give $z$ rotations. For example, $R_z(\alpha )R_y(\beta )R_z(\gamma )$ realizes any one-qubit unitary operator up to a global phase. Thus the atomic encoding admits arbitrary single-qubit quantum gates.

Rubidium is the chemical element with atomic number 37 and symbol $\mathrm{Rb}$. It is a alkali metal. It commonly forms a singly charged positive ion. Its optical transitions are useful in atomic spectroscopy and laser-cooling experiments, while rubidium-87 adds an experimentally useful isotope-specific nuclear-spin structure.^[ref]

Rubidium-87 is a long-lived radioactive isotope with thirty-seven protons and fifty neutrons. Its beta decay to strontium-87 supports rubidium-strontium geochronology.

It is also a common isotope in laser-cooled atomic-gas experiments. Its nuclear spin and hyperfine states provide experimentally accessible internal structure, while the whole atom can behave as a boson. These atomic roles are distinct from the geological use of its slow nuclear decay.

A qubit encoded in the two $m_F=0$ ground state hyperfine levels of rubidium-87. The electronic $J=1/2$ and nuclear spin $I=3/2$ combine to $F=1,2$. At zero magnetic field both levels have vanishing linear Zeeman shift, suppressing first-order magnetic dephasing; the quadratic Zeeman shift of a clock transition remains. Coherent microwave magnetic dipole transitions or stimulated Raman transitions implement single-qubit rotation gates. These are coupled electron-nucleus states, not bare nuclear-spin states.