Frequency stabilization of an atomic clock against variations of the C-field
The frequency of an atomic clock may be stabilized against C-field variation by applying a rf magnetic field perpendicular to the C-field to cause a coherent population transfer between Zeeman states that compensates for quadratic frequency shift of transitions of the clock. The cancellation, provided by a feed-forward mechanism, is exact. The invention can be implemented in any atomic clock by including an electrode in the clock generating a magnetic field perpendicular to the C-field, and providing an electronic circuit to send rf signals to the electrode.
1. A method of stabilizing frequency of an atomic clock against variations and non-uniformity of C-field, the method comprising applying microwave Ramsey pulses to a source of atoms before and after the atoms drift in the C-field along a trajectory to produce a microwave Ramsey signal, and applying a radiofrequency (rf) magnetic field perpendicular to the C-field to cause a coherent population transfer between Zeeman states that compensates for quadratic frequency shift of clock transition over a region defined by the trajectory between their interaction with two rf excitations of the rf magnetic field.
2. The method according to claim 1 , wherein the atomic clock has an atomic source that produces a continuous beam of atoms distributed over more than one magnetic state, and wherein population in adjacent states m F =−1 and m F =1 are used to produce the compensation for the quadratic frequency shift.
3. The method according to claim 2 , wherein electrodes generate the rf magnetic field over an entire Ramsey interrogation region over which the microwave Ramsey pulses are applied to the atoms, and the electrodes are powered by periodic rf current-pulses having a period with pulse-pairs timed to fit between the microwave Ramsey pulses.
4. The method according to claim 2 , wherein spatially separate electrodes continuously generate two rf magnetic field regions over which the atoms interact with the two rf excitations, the rf magnetic field regions separated by enough distance to fit between the microwave Ramsey pulses of a Ramsey interrogation region over which the microwave Ramsey pulses are applied to the atoms.
5. The method according to claim 1 , wherein the atomic source is pulsed and produces atoms in a single hyperfine state m F =0, and different Zeeman-splittings of lower and upper levels are used to produce the compensation for the quadratic frequency shift.
6. The method according to claim 5 , wherein electrodes generate the rf magnetic field over an entire Ramsey interrogation region over which the microwave Ramsey pulses are applied to the atoms, and the electrodes are powered by periodic rf current-pulses having a period with pulse-pairs timed to fit between the microwave Ramsey pulses.
7. The method according to claim 5 , wherein one electrode continuously generates one rf magnetic field region for generating at least one of the two rf excitations, located just above an a microwave Ramsey pulse.
8. The method according to claim 1 , wherein the atomic source produces a continuous beam of atoms in a single hyperfine state m F =0, and different Zeeman-splittings of lower and upper levels are used to produce the compensation for the quadratic frequency shift.
9. The method according to claim 8 , wherein electrodes generate the rf magnetic field over an entire Ramsey interrogation region over which the microwave Ramsey pulses are applied to the atoms, and the electrodes are powered by periodic rf current-pulses having a period with pulse-pairs timed to fit between the microwave Ramsey pulses.
10. The method according to claim 8 , wherein one electrode continuously generates one rf magnetic field region for generating at least one of two rf excitations, located just above a microwave Ramsey pulse.