1. Experiments with a single electron in storage ring T. Shaftan Fermilab, 2/21/2012

2. BINP team N. A. VinokurovP.V. Vorob’ov A.S. SokolovI.V. Pinayev V. M. PopikT. V. Shaftan These experiments were proposed and carried out under guidance of N. A. Vinokurov and P.V. Vorob’ov

3. 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.

4. 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

5. Can we use storage ring as a giant trap ?

6. VEPP-3 Storage Ring (BINP) Parameters VEPP-3 E inj =350 MeV F rev =4 MHz  =0.071  /  =4E-4  z =80 cm f RF =75 MHz Undulators L=3.4 m d=10 cm B max =5.4 kGs OK-4 FEL

7. How to get a single electron ? PMT Discriminator Counter Amplifier Undulators Time (many seconds) Photocounts per Second = Hz Photocounts t

8. 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 field versus time) Profile of potential energy Potential well Equation of motion:

9. 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 synchrotron oscillation amplitude and phase. Synchrotron Radiation effects:

10. Experiment I Semi-classical approach(SKL theory) “postulates”: oelectron is.-like object oquanta are emitted instantly oemission 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 ?

11. Quantum particle moving in a constant field and interacting with dissipative system Chang-Pu Sun and Li Hua Yu

12. Brown-Twiss Interferometer PMT A PMT B quanta photocounts

13. Experiment I e 11 Localization length e 22  undulator PMT1 PMT2 22 11  START STOP Time-to-digital Converter Number of events Time = Delays between START and STOP Storage ring Coincidence scheme

14. Results of experiment I Many electrons 5 electrons 2 electrons 1 electron Bunch of electrons in a short bunch mode: Time resolution of measurement Distributions of intervals between photocounts from PMT A and PMT B for different number of electrons Bunch length Bunch length width ~1ns Modern photodetectors: sub-picosecond resolution!

15. Results of experiment I For a large number of electrons we measure density distribution in the bunch (e A  e B events) For a few electrons we measure the distribution, dominated by (e A  e A 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

16. 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

17. Experiment II 1 2 3 VEPP-3 e Undulator PMT RF Master Oscillator START STOP 1 2 3 Time-to-digital Converter Number of STARTs Delays between START and STOP

18. Results of experiment II 1/1000 part of measured signal 0.5 ns 24.2 ns 0 ms6.4 ms 1 box= =0.5 ms x 0.45us Fast time: START-STOP “Slow” time in Lab frame

19. Data analysis T t T(t)=A(t)cos(wt)+B(t)sin(wt) A(t) B(t) Plane of the slow variables Assume, that A and B are constant during “window”= =only a few oscillation periods “window” Data spectrum

20. Some results of experiment II 740 Hz 618 Hz 540 Hz Nonisochronosity Amplitude distribution “Brownian” motion on the short time scale 4.6 ns 1.6 ns A Instantaneous frequency

21. Two electrons Measured data Data clean-up and analysis

22. 2 electrons: Reconstructed motion Amplitudes Phases 3.2 seconds 4 ns

23. 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 detector electronics photons in visible range High-energy  Superconducting dipole detector IOTA

24. An estimate for such experiment T. Shaftan’s PhD thesis Emissions of high-energy  s Energy time A fragment of synchrotron oscillation Energy450 MeV Revolution frequency 4 MHz Field in SC dipole6 T F synch600 Hz Bunch length80 cm Synch. damping time 90 msec

25. 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

26. 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 21 st 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

27. 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

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