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Cooling and self-excitation of a one-electron oscillator

Brian D’Urso

Published Jan 1, 2003• 11 citations
OpenAlex

Abstract

With a superposition of static electric and magnetic fields, a Penning trap can confine a single electron indefinitely. A weak coupling of the electron to its environment makes the system ideal for precision measurements but renders detection of the electron’s motion difficult. In order to measure fundamental properties of an electron, we employ a Penning trap cooled by a dilution refrigerator. This experimental setup requires extremely low-noise and low-power cryogenic amplifiers for detection of the electron’s axial motion. We design and demonstrate new amplifiers, resulting in a significant decrease of the axial temperature and in an improved signal to noise ratio. We use feedback to cool the axial motion and to self-excite the axial motion for continuous monitoring of the axial frequency. These techniques for cooling and measuring the axial frequency may contribute to an improved measurement of the electron g factor, a more stringent CPT test in leptons, and a more precise measurement of the proton-electron mass ratio.

Related papers

Toward sub-Kelvin resistive cooling and non destructive detection of trapped non-neutral electron plasma

S. Di Domizio, D. Krasnický, Vittorio Lagomarsino +3 more

A resonant circuit tuned to a particular frequency of the motion of charged particles stored in a Penning trap and connected to a low noise amplifier allows, at the same time, cooling and non destructive detection of the particles. Its use is widely diffused when single or few particles are stored near the centre of a hyperbolic Penning trap. We present a consistent model that predicts the shape of the induced signal when the tuned circuit is used to detect and cool the axial motion of a cold non neutral plasma stored in an open-ended cylindrical Penning trap. The model correctly accounts for the not negligible axial plasma size. We show that the power spectrum of the signal measured across the tuned circuit provides information about the particle number and insights about the plasma temperature. We report on the design of a HEMT-based cryogenic amplifier working at 14.4 MHz and 4.2 K and the results of the noise measurements. We have measured a drain current noise in the range from 6 to 17 pA/√Hz, which corresponds to an increase of the tuned circuit equivalent temperature of at maximum 0.35 K. The cryogenic amplifier has a very low power consumption from few tens to few hundreds of μW corresponding to a drain current in the range 100–800 μ A . An additional contribution due to the gate noise has been identified when the drain current is below 300 μA; above that value an upper limit of the increase of the equivalent tuned circuit temperature due to this contribution of 0.02 K has been obtained. These features make the tuned circuit connected to this amplifier a promising device for detecting and cooling the axial motion of an electron plasma when the Penning trap is mounted inside a dilution refrigerator.

Journal of Instrumentation•Jan 1, 2015•4 citations

Single-Particle Self-Excited Oscillator

Brian D’Urso, Ramon van Handel, Brian Odom +2 more

Electronic feedback is used to self-excite the axial oscillation of a single electron in a Penning trap. Large, stable, easily detected oscillations arise even in an anharmonic potential. Amplitudes are controlled by adjusting the feedback gain, and frequencies can be made nearly independent of amplitude fluctuations. Quantum jump spectroscopy of a perpendicular cyclotron motion reveals the absolute temperature and amplitude of the self-excited oscillation. The possibility to quickly measure parts per billion frequency shifts could open the way to improved measurements of e(-), e(+), p, and (-)p magnetic moments.

Physical Review Letters•Mar 23, 2005•34 citations

Thermometry of 9Be+ ions in a cryogenic Penning trap

J. Mielke

High precision comparisons of the proton and antiproton g-factor enable stringent tests of CPT symmetry in the baryonic sector. However, current measurement routines suffer from long preparation times and high particle temperatures, which complicate the increase of the precision beyond the parts per billion regime. As a solution, new sympathetic cooling schemes based on co-trapped laser-cooled ions may be used to cool (anti-)protons to the ground state of motion and to significantly decrease particle preparation times. In addition, motional coupling to an auxiliary ion in a double-well potential can be used for the implementation of new readout schemes based on quantum logic spectroscopy for the spin-state of the (anti-)protons. This thesis describes a cryogenic Penning trap system for ground state cooling of single 9Be+ ions, which represents the latest development of the BASE experiment in Hannover towards the implementation of sympathetic cooling schemes and quantum logic spectroscopy of single (anti-)protons. Furthermore, the setup and implementation of lasers systems at 313nm for Doppler cooling, repumping and Raman interactions are described. To this end, an optical platform for laser beam delivery to the vacuum system and an optical phase-locked loop for the stabilization of the relative phase of two lasers at 313 nm are presented. In this work, the laser systems are used for measurements of the optical resonance frequencies for cooling, probing and repumping of 9Be+ ions. In addition, stimulated Raman transitions are demonstrated using two phase-locked lasers at 313nm. In the following, this technique is used for high-precision measurements of the qubit frequency and the magnetic field, as well as themometry measurements with 9Be+ ions. The temperature of the ions after Doppler cooling is measured as a function of the cooling laser parameters and a minimal axial mode temperature of 1.77(10) mK is obtained. The results of this thesis pave the way for sideband spectroscopy and ground state cooling of single 9Be+ ions in Penning traps, which is an essential prerequisite for sympathetic ground state cooling of single (anti-)protons and the application of quantum logic spectroscopy to (anti-)proton g-factor measurements in the future.

•Jan 1, 2021•0 citations

Cavity control in a single-electron quantum cyclotron

David Hanneke

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.

•Jan 1, 2007•0 citations

Resolved-sideband cooling of a single Be + 9 ion in a cryogenic multi-Penning-trap for discrete symmetry tests with (anti-)protons

Juan M. Cornejo, Johannes Brombacher, Julia A. Coenders +5 more

Manipulating the motion of individual trapped ions at the single quantum level has become standard practice in radio-frequency ion traps, enabling sweeping advances in quantum information processing and precision metrology. The key step for motional-state engineering is ground-state cooling. Full motional control also bears great potential to explore another regime of sensitivities for fundamental physics tests in Penning traps. Here we demonstrate the key enabling step by implementing resolved-sideband cooling on the axial mode of a single Be + 9 ion in a 5 Tesla cryogenic Penning trap. The system has been developed for the implementation of high-precision antimatter experiments to test the fundamental symmetries of the standard model with the highest accuracy in the baryonic sector. We measure an axial phonon number of n ¯ z = 0.10 ( 4 ) after cooling and demonstrate that the axial heating rate in our system is compatible with the implementation of quantum logic spectroscopy of (anti-)protons. Published by the American Physical Society 2024

Physical Review Research•Sep 3, 2024•10 citations

Eliminating cavity shifts from electron magnetic moment (g-2) measurements

G. Gabrielse

A cylindrical Penning trap is of such high quality that a single electron is observed with good signal-to-noise. The trap is also a good approximation to an ideal cylindrical microwave cavity. This is documented in situ at 4 K with a new probe utilizing trapped electrons. An extraordinary control of the cavity-electron interaction results and opens the way to a new generation of electron magnetic moment measurements, not limited by either cavity frequency shifts or damping widths, and to sideband cooling of an electron motion to very low (mK) temperatures.

Bulletin of the American Physical Society•May 1, 1993•0 citations
With a superposition of static electric and magnetic fields, a Penning trap can confine a single electron indefinitely. A weak coupling of the electron to its environment makes the system ideal for precision measurements but renders detection of the electron’s motion difficult. In order to measure fundamental properties of an electron, we employ a Penning trap cooled by a dilution refrigerator. This experimental setup requires extremely low-noise and low-power cryogenic amplifiers for detection of the electron’s axial motion. We design and demonstrate new amplifiers, resulting in a significant decrease of the axial temperature and in an improved signal to noise ratio. We use feedback to cool the axial motion and to self-excite the axial motion for continuous monitoring of the axial frequency. These techniques for cooling and measuring the axial frequency may contribute to an improved measurement of the electron g factor, a more stringent CPT test in leptons, and a more precise measurement of the proton-electron mass ratio.
A resonant circuit tuned to a particular frequency of the motion of charged particles stored in a Penning trap and connected to a low noise amplifier allows, at the same time, cooling and non destructive detection of the particles. Its use is widely diffused when single or few particles are stored near the centre of a hyperbolic Penning trap. We present a consistent model that predicts the shape of the induced signal when the tuned circuit is used to detect and cool the axial motion of a cold non neutral plasma stored in an open-ended cylindrical Penning trap. The model correctly accounts for the not negligible axial plasma size. We show that the power spectrum of the signal measured across the tuned circuit provides information about the particle number and insights about the plasma temperature. We report on the design of a HEMT-based cryogenic amplifier working at 14.4 MHz and 4.2 K and the results of the noise measurements. We have measured a drain current noise in the range from 6 to 17 pA/√Hz, which corresponds to an increase of the tuned circuit equivalent temperature of at maximum 0.35 K. The cryogenic amplifier has a very low power consumption from few tens to few hundreds of μW corresponding to a drain current in the range 100–800 μ A . An additional contribution due to the gate noise has been identified when the drain current is below 300 μA; above that value an upper limit of the increase of the equivalent tuned circuit temperature due to this contribution of 0.02 K has been obtained. These features make the tuned circuit connected to this amplifier a promising device for detecting and cooling the axial motion of an electron plasma when the Penning trap is mounted inside a dilution refrigerator.
Electronic feedback is used to self-excite the axial oscillation of a single electron in a Penning trap. Large, stable, easily detected oscillations arise even in an anharmonic potential. Amplitudes are controlled by adjusting the feedback gain, and frequencies can be made nearly independent of amplitude fluctuations. Quantum jump spectroscopy of a perpendicular cyclotron motion reveals the absolute temperature and amplitude of the self-excited oscillation. The possibility to quickly measure parts per billion frequency shifts could open the way to improved measurements of e(-), e(+), p, and (-)p magnetic moments.
High precision comparisons of the proton and antiproton g-factor enable stringent tests of CPT symmetry in the baryonic sector. However, current measurement routines suffer from long preparation times and high particle temperatures, which complicate the increase of the precision beyond the parts per billion regime. As a solution, new sympathetic cooling schemes based on co-trapped laser-cooled ions may be used to cool (anti-)protons to the ground state of motion and to significantly decrease particle preparation times. In addition, motional coupling to an auxiliary ion in a double-well potential can be used for the implementation of new readout schemes based on quantum logic spectroscopy for the spin-state of the (anti-)protons. This thesis describes a cryogenic Penning trap system for ground state cooling of single 9Be+ ions, which represents the latest development of the BASE experiment in Hannover towards the implementation of sympathetic cooling schemes and quantum logic spectroscopy of single (anti-)protons. Furthermore, the setup and implementation of lasers systems at 313nm for Doppler cooling, repumping and Raman interactions are described. To this end, an optical platform for laser beam delivery to the vacuum system and an optical phase-locked loop for the stabilization of the relative phase of two lasers at 313 nm are presented. In this work, the laser systems are used for measurements of the optical resonance frequencies for cooling, probing and repumping of 9Be+ ions. In addition, stimulated Raman transitions are demonstrated using two phase-locked lasers at 313nm. In the following, this technique is used for high-precision measurements of the qubit frequency and the magnetic field, as well as themometry measurements with 9Be+ ions. The temperature of the ions after Doppler cooling is measured as a function of the cooling laser parameters and a minimal axial mode temperature of 1.77(10) mK is obtained. The results of this thesis pave the way for sideband spectroscopy and ground state cooling of single 9Be+ ions in Penning traps, which is an essential prerequisite for sympathetic ground state cooling of single (anti-)protons and the application of quantum logic spectroscopy to (anti-)proton g-factor measurements in the future.
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.
Manipulating the motion of individual trapped ions at the single quantum level has become standard practice in radio-frequency ion traps, enabling sweeping advances in quantum information processing and precision metrology. The key step for motional-state engineering is ground-state cooling. Full motional control also bears great potential to explore another regime of sensitivities for fundamental physics tests in Penning traps. Here we demonstrate the key enabling step by implementing resolved-sideband cooling on the axial mode of a single Be + 9 ion in a 5 Tesla cryogenic Penning trap. The system has been developed for the implementation of high-precision antimatter experiments to test the fundamental symmetries of the standard model with the highest accuracy in the baryonic sector. We measure an axial phonon number of n ¯ z = 0.10 ( 4 ) after cooling and demonstrate that the axial heating rate in our system is compatible with the implementation of quantum logic spectroscopy of (anti-)protons. Published by the American Physical Society 2024
A cylindrical Penning trap is of such high quality that a single electron is observed with good signal-to-noise. The trap is also a good approximation to an ideal cylindrical microwave cavity. This is documented in situ at 4 K with a new probe utilizing trapped electrons. An extraordinary control of the cavity-electron interaction results and opens the way to a new generation of electron magnetic moment measurements, not limited by either cavity frequency shifts or damping widths, and to sideband cooling of an electron motion to very low (mK) temperatures.