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Physical Review Letters

Observing the Quantum Limit of an Electron Cyclotron: QND Measurements of Quantum Jumps between Fock States

Steven Peil, G. Gabrielse

Published Aug 16, 1999• 208 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.83.1287

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

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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
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 quantum cyclotron is one trapped electron or positron that occupies only its lowest cyclotron and spin states. A master equation is solved for a driven quantum cyclotron with a QND (quantum nondemolition) coupling to a detection oscillator in thermal equilibrium, the latter making this an open quantum system. The predicted rate of a cyclotron and spin quantum jumps as a function of drive frequency, for a small coupling between the detection motion and its thermal reservoir, differs sharply from what has been predicted and used for past measurements. The calculation suggests a ten times more precise electron magnetic moment measurement is possible, as needed to investigate current differences between the most precise prediction of the standard model of particle physics, and the most accurate measurement of a property of an elementary particle.
Detector backaction can be completely evaded when the state of a one-electron quantum cyclotron is detected, but it nonetheless significantly broadens the quantum-jump resonance line shapes from which the cyclotron frequency can be deduced. This limits the accuracy with which the electron magnetic moment can be determined to test the standard model's most precise prediction. A steady-state solution to a master equation, the first quantum calculation for the open quantum cyclotron system, illustrates a method to circumvent the detection backaction upon the measured frequency.