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Quantum Electronics and Laser Science Conference

QND observation of quantum jumps between Fock states: a one-electron cyclotron oscillator at 70 mK to 4.2 K

G. Gabrielse, Steven Peil, Brian Odom, Brian D’Urso

Published Jan 20, 2003• 1 citation
Publisher

Abstract

Summary form only given. A one-electron cyclotron oscillator is cooled to thermal equilibrium at temperatures between 70 mK and 4.2 K - the first time that an isolated elementary particle has been cooled below 4.2 K. Continuous quantum non-demolition (QND) measurements of the electron cyclotron energy reveal the equilibrium oscillator in a quantum Fock state, with occasional and abrupt quantum jumps to adjacent Fock states, stimulated by blackbody photons in the cavity.

DOI
10.1109/qels.1999.807109

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Summary form only given. A one-electron cyclotron oscillator is cooled to thermal equilibrium at temperatures between 70 mK and 4.2 K - the first time that an isolated elementary particle has been cooled below 4.2 K. Continuous quantum non-demolition (QND) measurements of the electron cyclotron energy reveal the equilibrium oscillator in a quantum Fock state, with occasional and abrupt quantum jumps to adjacent Fock states, stimulated by blackbody photons in the cavity.
Quantum jumps between Fock states of a one-electron oscillator reveal the quantum limit of a cyclotron. With a surrounding cavity inhibiting synchrotron radiation 140-fold, the jumps show a 13 s Fock state lifetime and a cyclotron in thermal equilibrium with 1.6 to 4.2 K blackbody photons. These disappear by 80 mK, a temperature 50 times lower than previously achieved with an isolated elementary particle. The cyclotron stays in its ground state until a resonant photon is injected. A quantum cyclotron offers a new route to measuring the electron magnetic moment and the fine structure constant.
Quantum jumps between Fock states of a one-electron oscillator reveal the quantum limit of a cyclotron accelerator. The states live for seconds when spontaneous emission is inhibited by 140 within a cylindrical Penning trap cavity. Averaged over hours the oscillator is in thermal equilibrium with black-body photons in the cavity. At 80 mK, quantum jumps occur only when resonant microwave photons are introduced into the cavity, opening a route to improved measurements of the magnetic moments of the electron and positron. The temperature demonstrated is about 60 times lower than the 4.2 K temperature at which charged elementary particles were previously stored. Implications for the production of cold antihydrogen are discussed.
Fock states of a oneelectron cyclotron oscillator have been produced and observed nondestructively The states are longlived because spontaneous emission is inhib ited by a factor of using the modied radiation eld of a cylindrical Penning trap Direct nondestructive observation is achieved with a magnetic gradient that is ten times larger than previously possible allowing the states to be resolved with high signaltonoise ratio Quantum jumps up to the n cyclotron level have been observed The potential line broadening from the increased magnetic cou pling is avoided because we have lowered the temperature to which electrons can be cooled by nearly two orders of magnitude to as low as \t mK This is the rst time a trapped elementary particle has been cooled below K At these low temperatures the cyclotron oscillator is completely cooled to its ground state Detection of the electron signal is made possible by a lowpower transistor that was developed in collaboration with condensedmatter colleagues Applications include
The quantum non-demolition measurement of the cyclotron excitations of an electron trapped in a Penning trap is shown to be accessible, with the modern technology, by only considering the coupling between the axial and the cyclotron motions induced by the relativistic correction to the electron's mass. It is shown that such a measurement is possible only when the spin state of the electron is preassigned and the wave function will then collapse into a Fock state. When this is not the case the wave function of the electron will collapse into an entangled state.
A single electron in a quantum cyclotron yields new measurements of the electron magnetic moment, given by g/2 = 1.00115965218073(28)[0.28 ppt], and the fine structure constant, α −1 = 137.035999084(51)[0.37 ppb], both significantly improved from prior results. The static magnetic and electric fields of a Penning trap confine the electron, and a 100 mK dilution refrigerator cools its cyclotron motion to the quantum-mechanical ground state. A quantum nondemolition measurement allows resolution of single cyclotron jumps and spin flips by coupling the cyclotron and spin energies to the frequency of the axial motion, which is self-excited and detected with a cryogenic amplifier. The trap electrodes form a high-Q microwave resonator near the cyclotron frequency; coupling between the cyclotron motion and cavity modes can inhibit spontaneous emission by over 100 timesthe free-space rate and shiftthe cyclotron frequency, a systematic effect that dominated the uncertainties of previous g-value measurements. A cylindrical trap geometry creates cavity modes with analytically calculable couplingsto cyclotron motion. Two independent methods use the cyclotron damping rate of an electron plasma or of the single electron itself as probes of the cavity mode structure and allow the identification ofthe modes by their geometries and couplings, the quantification of an offset between the mode and electrostatic centers, and the reduction of the cavity shift uncertainty to sub-dominant levels. Measuring g at four magnetic fields with cavity shifts spanning thirty times the final g-value uncertainty provides a check on the calculated cavity shifts. Magnetic field fluctuations limit the measurement of g by adding a noise-model dependence to the extraction of the cyclotron and anomaly frequencies from their resonance lines; the relative agreement of two line-splitting methods quantifies a lineshape model uncertainty. New techniques promise to increase field stability, narrow the resonance lines, and accelerate the measurement cycle. The measured g allows tests for physics beyond the Standard Model through searches for its temporal variation and comparisons with a “theoretical” g-value calculated from quantum electrodynamics and an independently measured fine structure constant.
A microscopic system under continuous observation exhibits at random times sudden jumps between its states. The detection of this essential quantum feature requires a quantum non-demolition (QND) measurement1, 2, 3 repeated many times during the system evolution. Quantum jumps of trapped massive particles (electrons, ions or molecules4,5,6,7,8) have been observed, which is not the case of the jumps of light quanta. Usual photodetectors absorb light and are thus unable to detect the same photon twice. They must be replaced by a transparent counter 'seeing' photons without destroying them3. Moreover, the light has to be stored over a duration much longer than the QND detection time. We have fulfilled these challenging conditions and observed photon number quantum jumps. Microwave photons are stored in a superconducting cavity for times in the second range. They are repeatedly probed by a stream of non-absorbing atoms. An atom interferometer measures the atomic dipole phase shift induced by the non-resonant cavity field, so that the final atom state reveals directly the presence of a single photon in the cavity. Sequences of hundreds of atoms highly correlated in the same state, are interrupted by sudden state-switchings. These telegraphic signals record, for the first time, the birth, life and death of individual photons. Applying a similar QND procedure to mesoscopic fields with tens of photons opens new perspectives for the exploration of the quantum to classical boundary9, 10.