Experiments with a single electron in storage ring

T. Shaftan

Fermilab, 2/21/2012

BINP team

N. A. Vinokurov P.V. Vorob’ov

A.S. Sokolov I.V. Pinayev

V. M. Popik T. V. Shaftan

These experiments were proposed and carried out under guidance of N. A. Vinokurov and P.V. Vorob’ov

The traps of Paul and Dehmelt (Nobel Prize 1989)

http://www.nobel.se/physics/educational/poster/1989/trap.html

  The works of Wolfgang Paul, which led to the Paul trap, are based on investigations of the properties of electric and magnetic multipoles. Paul has shown that a magnetic hexapole focuses beams of atoms having a magnetic dipole moment.    The electric quadrupole: a d.c. voltage in addition to an a.c. voltage is applied to the electrode pairs A-A. To the other electrode pair B-B the same voltages with opposite signs are applied. The Paul trap now being used by many scientists for storing ions may be considered a three-dimensional version of the two-dimensional mass filter.

Hans Dehmelt's contributions are mainly connected with the development and use of the Penning trap. He invented ingenious methods of cooling, perturbing, storing (one single electron was trapped for more than 10 months), and communicating with the trapped particles, thus forcing them to reveal their properties.

In the combined electric and magnetic field in the Penning trap charged particles describe a complicated motion, which consists of three independent oscillations; one axial, one cyclotron, and one magnetron oscillation, each one having a well defined frequency.

The axial oscillation induces a signal in the end electrodes. This signal is sensitive to the total number of charged particles in the cloud. By shining high frequency radiation into the trap it is possible to flip the electron dipole moment repeatedly (fig. 3). Furthermore, it is possible to "lift" the electron in the quantized cyclotron orbits which the electron actually occupies. With one single electron in the trap it has been possible to compare the resonance frequencies of these two events, the flip and the "lift", thus deriving the so called g-factor.

The g-factor has been determined with twelve significant digits and is now the most accurately known fundamental constant. One may use similar methods when comparing the masses of particles with a very high precision.

 

Frequencies:

     the cyclotron oscillation:         24 MHz

      the axial oscillation:              360 kHz

      the magnetron oscillation:      2.5 kHz

Experiments with single particles: Paul and Penning traps

particle trajectory

Can we use storage ring as a giant trap ?

VEPP-3 Storage Ring (BINP)Parameters

VEPP-3

Einj=350 MeVFrev=4 MHz=0.071/=4E-4z=80 cmfRF=75 MHz

Undulators

L=3.4 md=10 cmBmax=5.4 kGs

OK-4 FEL

How to get a single electron ?

PMT

Discriminator

Counter

Amplifier

Undulators

Time (many seconds)Time (many seconds)

Photocounts per Second = Hz

Photocounts

t

Longitudinal motion in circular accelerator

FIG. 37--Phase diagram for large oscillations. Bounded energy oscillations occur only inside of the separatrix.

Arbitrary RF waveform (Accelerating electric fieldversus time)

Profile of potential energyPotential well

022

2

t

Equation of motion:

Semi-classical description (Sands, Kolomensky&Lebedev, ~1950)

“Jump” of energy oscillation due to photon emission

Quantum fluctuations of synchrotron radiation prevent electron phase space from collapse due to adiabatic damping and lead to a diffusion of synchrotronoscillation amplitude and phase.

)(22

2

tFtt

SynchrotronRadiation effects:

Experiment I

• Semi-classical approach(SKL theory) “postulates”:o electron is .-like objecto quanta are emitted instantlyo emission of quanta is a Poissonian process

• There is no complete quantum description and “…However, a proper QED analysis has not yet been obtained (and maybe, those do not even exist).” (K.J. Kim and A. Sessler, The Equation of motion of an Electron, 1998).

• Photon statistics: What is the correlation length of UR intensity for different number of electrons and for a single one ?

• How a single electron’s wavepacket is localized: is it -like ? Or is it comparable with the potential well width ?

Quantum particle moving in a constant field and interacting with dissipative system

Chang-Pu Sun and Li Hua Yu

Brown-Twiss Interferometer

dttItI )()()(

PMT A

PM

T B

)()()|( tItItt

quanta

photocounts

Experiment I

e1

Localizationlength

e2

undulator

PMT1

PMT22

1

START

STOP

Time-to-digital Converter

Num

ber

of e

vent

sTime = Delays between START and STOP

Storage ringCoincidencescheme

Results of experiment I

Many electrons

5 electrons

2 electrons

1 electron

Bunch of electrons in a short bunch mode:Time resolutionof measurement

Distributions of intervals between photocounts from PMT A and PMT B for different number of electrons

Bunchlength

Bunchlength

width

~1ns

Modern photodetectors: sub-picosecond resolution!

Results of experiment I

• For a large number of electrons we measure density distribution in the bunch (eAeB events)

• For a few electrons we measure the distribution, dominated by (eAeA events)

• For a single electron the width of the distribution is equal to the time resolution

• Correlation length of UR intensity for a single electron is measured to be much shorter than natural bunch length

• Interpretation: localization length of a single electron is much shorter than the bunch length

• How short is the localization length? Needs further studies with better time resolution

Experiment II

• Study a stochastic process of synchrotron oscillation, driven by “quantum” noise

• Record electron’s motion at the discrete moments of time

• Reconstruct amplitude and slow phase of the motion

• Obtain correlations

• Experiments with two electrons simultaneously: to exclude “technical” noise and analyze cross-correlations between electrons

Experiment II

1 2 3

VEPP-3

e

UndulatorPMT

RFMasterOscillator

START

STOP

123

Time-to-digital Converter

Num

ber

of S

TA

RT

s

Delays between START and STOP

Results of experiment II

1/1000 part of measured signal

0.5 ns

24.2 ns

0 ms 6.4 ms

1 box==0.5 ms x 0.45us

Fast time: START-STOP

“Slow” timein Lab frame

Data analysis

T

t

T(t)=A(t)cos(wt)+B(t)sin(wt)

A(t)

B(t)

Plane of the slowvariables

Assume, that A and B areconstant during “window”==only a few oscillation periods

“window”Data spectrum

Some results of experiment II

740 Hz

618 Hz

540 Hz

Nonisochronosity

Amplitudedistribution

“Brownian”motion on theshort time scale

4.6 ns 1.6 ns

A

Instantaneousfrequency

Two electrons

Measured data

Data clean-upand analysis

2 electrons: Reconstructed motion

Amplitudes

Phases

3.2 seconds

4 ns

4 ns

Considerations for design of the storage ring for experiments with a single electron

• Medium energy: photon wavelength and flux are sufficient for detection of electron’s coordinates

• Increase flux of emitted high-energy quanta so that the electron’s dynamics will be governed by these emissions

• Long bunch length or large transverse beam size so to maximize the “contrast” above the time- or spatial resolution of the photon detection system

A concept of the specialized ring with a strong dipole

undulator

detectorelectronics

photons invisible range

High-energy

Superconducting dipoledetector

IOTA

An estimate for such experiment

T. Shaftan’s PhDthesis

Emissions of high-energy s

Energy

time

A fragment of synchrotron oscillation

Energy 450 MeV

Revolution frequency

4 MHz

Field in SC dipole 6 T

F synch 600 Hz

Bunch length 80 cm

Synch. damping time

90 msec

Summary• We demonstrated possibility of studying dynamics of a single

particle in a storage ring

• Experiment I: Correlation length of quanta emitted by a single electron is measured to be less than the natural bunch length

• Experiment II: Stochastic process of synchrotron oscillation has been studied; characteristics of diffusion induced by quantum fluctuations are obtained

• Design of an optimized storage ring will enable new exciting experiments with a single electron

Conclusion• Quantum measurement process and associated localization of the

particle’s wavefunction – considered by (e.g.) V. Ginzburg (and many others) as one of three most important problems of physics in 21st century.

• Modern experimental physics is lacking appropriate experiments to shed light on this subject

• Single electron in storage ring presents a model of a single particle interacting with environment and being registered via quantum measurement process

• Modern methods of light detection enable detection of photons with high sensitivity, sub-picosecond resolution and large event count

• New experiments with a single electron may lead to a breakthrough in understanding of basic principles of quantum physics

References• Some related theoretical work

– A.O. Caldeira and A.J. Leggett, Path Integral Approach to Quantum Brownian Motion, Physica 121A (1983), 587-616

– L.H. Yu et al., Exact Dynamics of a Quantum Dissipative System in a Constant External Field, Phys Rev A V51, N3 (1995)

– S. V. Feleev, Reduction of the wavepacket of a relativistic charged particle by emission of a photon, arXiv: hep-ph/9706372v1 16 June 1997

• Experimental work – I. V. Pinayev et al., Experiments with undulator radiation of a single electron, Nucl. Instr.

and Meth. A341 (1994) 17-20

– A. N. Aleshaev et al. A study of the influence of synchrotron radiation quantum fluctuations on the synchrotron oscillations of a single electron using undulator radiation, Nucl. Instr. and Meth. A359 (1995) 80-84

– I. V. Pinayev et al., A study of the influence of the stochastic process on the synchrotron oscillations of a single electron, circulated in the VEPP-3 storage ring, Nucl. Instr. and Meth. A375 (1996) 71-73

Quantum oscillator in the potential well,coupled with thermostat (by L.H. Yu)