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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 3967–3974
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Spatial coherence of electron bunches extracted from an arbitrarily shaped cold atom electron source

Sebastian D. Saliba, Corey T. Putkunz, David V. Sheludko, Andrew J. McCulloch, Keith A. Nugent, and Robert E. Scholten  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 3967-3974 (2012)
http://dx.doi.org/10.1364/OE.20.003967


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Abstract

We describe the spatial coherence properties of a cold atom electron source in the framework of a quasihomogeneous wavefield. The model is used as the basis for direct measurements of the transverse spatial coherence length of electron bunches extracted from a cold atom electron source. The coherence length is determined from the measured visibility of a propagated electron distribution with a sinusoidal profile of variable spatial frequency. The electron distribution was controlled via the intensity profile of an atomic excitation laser beam patterned with a spatial light modulator. We measure a lower limit to the coherence length at the source of lc = 7.8 ± 0.9 nm.

© 2012 OSA

1. Introduction

Electron probes are an important tool for nanometre scale investigations, for example the determination of membrane protein structures [1

1. R. Henderson and P. N. T. Unwin, “Three-dimensional model of purple membrane obtained by electron microscopy,” Nature 257, 28–32 (1975). [CrossRef] [PubMed]

]. Improvements in electron sources have enabled increased spatial and temporal resolution beyond optical alternatives [2

2. B. G. Levi, “Focus on improving transmission electron microscopes starts to pay off,” Phys. Today 63, 15–19 (2010). [CrossRef]

]. In particular, ultrafast electron diffraction (UED) is an emerging technique for obtaining atomic-level structural dynamics at sub-picosecond timescales, such as atomic motion and phase transitions [3

3. H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, and A. H. Zewail, “Direct imaging of transient molecular structures with ultrafast diffraction,” Science 291, 458–463 (2001). [CrossRef] [PubMed]

5

5. B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003). [CrossRef] [PubMed]

]. Ultrafast diffraction also has the potential to capture images before sample damage occurs, essential to imaging biological specimens with sub-nanometre resolution [6

6. H. M. Quiney and K. A. Nugent, “Biomolecular imaging and electronic damage using X-ray free-electron lasers,” Nat. Phys. 7, 142–146 (2011). [CrossRef]

, 7

7. 2.M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, J.-M. Claverie, C. Bostedt, J. D. Bozek, S. Boutet, A. A. Miahnahri, M. Messerschmidt, J. Krzywinski, G. Williams, K. O. Hodgson, M. J. Bogan, C. Y. Hampton, R. G. Sierra, D. Starodub, I. Andersson, S. Bajt, M. Barthelmess, J. C. H. Spence, P. Fromme, U. Weierstall, R. Kirian, M. Hunter, R. Bruce Doak, Stefano Marchesini, Stefan P. Hau-Riege, Matthias Frank, Robert L. Shoeman, Lukas Lomb, Sascha W. Epp, Robert Hartmann, Daniel Rolles, A. Rudenko, C. Schmidt, L. Foucar, N. Kimmel, P. Holl, B. Rudek, B. Erk, A. Homke, C. Reich, D. Pietschner, G. Weidenspointner, L. Struder, G. Hauser, H. Gorke, J. Ullrich, I. Schlichting, S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K.-U. Kuhnel, R. Andritschke, C.-D. Schroter, F. Krasniqi, M. Bott, S. Schorb, Da. Rupp, M. Adolph, T. Gorkhover, H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, H. N. Chapman, and J. Hajdu, “Single mimivirus particles intercepted and imaged with an X-ray laser,” Nature 470, 78–81 (2011). [CrossRef] [PubMed]

].

Carbon nanotube (CNT) field emitters are currently the brightest available electron sources, though must operate at low currents to avoid Coulomb expansion and are therefore not suitable for ultrafast imaging [8

8. P. Piot, “Review of experimental results on high-brightness photo-emission electron sources,” in The Physics and Applications of High Brightness Electron Beams, J. Rosenzweig, ed. (World Scientific, 2003), pp. 127–142. [CrossRef]

,9

9. N. de Jonge, M. Allioux, J. T. Oostveen, K. B. Teo, and W. I. Milne, “Optical performance of carbon-nanotube electron sources,” Phys. Rev. Lett. 94, 186807 (2005). [CrossRef] [PubMed]

]. Conventional photoemission sources use high energy laser pulses to generate hot electrons at high current. Recently, sub-100 fs 0.25 pC electron bunches have been extracted from a photoemission source, enabling demonstration of single-shot diffraction from a crystalline gold foil [10

10. T. van Oudheusden, P. L. E. M. Pasmans, S. B. van der Geer, M. J. de Loos, M. J. van der Wiel, and O. J. Luiten, “Compression of subrelativistic space-charge-dominated electron bunches for single-shot femtosecond electron diffraction,” Phys. Rev. Lett. 105, 264801 (2010). [CrossRef]

].

Electron bunches extracted from cold atoms provide a new and intrinsically different source for UED imaging [11

11. B. J. Claessens, S. B. van der Geer, G. Taban, E. J. D. Vredenbregt, and O. J. Luiten, “Ultracold electron source,” Phys. Rev. Lett. 95, 164801 (2005). [CrossRef] [PubMed]

13

13. A. J. McCulloch, D. V. Sheludko, S. D. Saliba, S. C. Bell, M. Junker, K. A. Nugent, and R. E. Scholten, “Arbitrarily shaped high-coherence electron bunches from cold atoms,” Nat. Phys. 7, 785–788 (2011). [CrossRef]

]. In a cold atom electron source (CAES), electrons are extracted by photoionization of laser cooled and trapped atoms (temperature T < 100μK). The predicted upper limit to transverse normalized brightness for these sources is comparable to that of CNT emission sources, but with significantly higher electron flux [14

14. O. J. Luiten, B. J. Claessens, S. B. van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, “Ultracold electron sources,” Int. J. Mod. Phys. A 22, 3882–3897 (2007). [CrossRef]

].

Conventional electron sources are initially incoherent, and useful coherence is obtained only as a consequence of propagation, described by the van Cittert-Zernike theorem. A CAES produces very low temperature electrons (T < 15 K [13

13. A. J. McCulloch, D. V. Sheludko, S. D. Saliba, S. C. Bell, M. Junker, K. A. Nugent, and R. E. Scholten, “Arbitrarily shaped high-coherence electron bunches from cold atoms,” Nat. Phys. 7, 785–788 (2011). [CrossRef]

]) with small initial transverse momentum spread, and consequently the transverse spatial coherence is large at the source. As with conventional electron sources, the CAES coherence can then be further enhanced by propagation, and the flux of a CAES can be many orders of magnitude greater than single-atom field emitters. The CAES therefore has promising properties desirable for diffractive imaging, including sufficient intrinsic transverse spatial coherence for imaging whole biomolecules coupled with the potential for high brightness.

An electron bunch extracted from a CAES has the properties of a partially coherent quasi-homogeneous wavefield. While the temperature of these cold electron bunches has previously been measured and a transverse spatial coherence length inferred [13

13. A. J. McCulloch, D. V. Sheludko, S. D. Saliba, S. C. Bell, M. Junker, K. A. Nugent, and R. E. Scholten, “Arbitrarily shaped high-coherence electron bunches from cold atoms,” Nat. Phys. 7, 785–788 (2011). [CrossRef]

], in this paper we directly measure the transverse spatial coherence by mapping out the form of the coherence function, thus confirming the basic property which makes these new sources important for diffractive imaging. We measure the visibility of a propagated electron distribution with a sinusoidal profile, created at the source by directly modifying the excited state atomic distribution [13

13. A. J. McCulloch, D. V. Sheludko, S. D. Saliba, S. C. Bell, M. Junker, K. A. Nugent, and R. E. Scholten, “Arbitrarily shaped high-coherence electron bunches from cold atoms,” Nat. Phys. 7, 785–788 (2011). [CrossRef]

]. This profile can be rapidly varied to allow measurements over a wide range of spatial frequencies. The variation in the visibility of the propagated electron profile with spatial frequency is shown to relate to the coherence function in close analogy to the visibility of a two-slit interference fringe pattern commonly used to characterize source coherence [15

15. D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001). [CrossRef]

, 16

16. K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99(99) (2010). [CrossRef]

].

2. A cold atom electron source

2.1. Experimental description

In our experiments, approximately 109 Rb85 atoms in a magneto-optical trap (T = 70μK) were excited from the 5S1/2(F = 3) ground state to the 5P3/2(F′ = 4) excited state using a laser of wavelength 780nm (Fig. 1). The intensity profile of the excitation laser beam was shaped using a phase-only spatial light modulator (SLM) to selectively excite a desired density distribution of atoms within the Rb cloud [13

13. A. J. McCulloch, D. V. Sheludko, S. D. Saliba, S. C. Bell, M. Junker, K. A. Nugent, and R. E. Scholten, “Arbitrarily shaped high-coherence electron bunches from cold atoms,” Nat. Phys. 7, 785–788 (2011). [CrossRef]

]. The shaped, excited atom distribution was photoionized using a 5ns 480nm wavelength laser pulse, spatially uniform to 3% across the cloud. The electrons were accelerated in a uniform electric field (F = 40kV/m, distance 2.5 cm, final energy 1 keV) parallel to the excitation laser and propagated 22 cm in a null field. The spatial distribution of the electron pulse was observed on a phosphor screen attached to a micro channel plate (MCP) charge amplifier.

Fig. 1 Schematic of the cold atom electron source, showing the cold atom magneto-optic trap, electrostatic accelerator plates, spatial light modulator (SLM) and detector. The atom cloud was excited by a 780 nm laser along the electron acceleration axis. The excitation laser was shaped using the SLM to select a spatial profile of cold atoms with a sinusoidal variation in one transverse direction and a constant amplitude in the other transverse direction (see also Fig. 3). A 480 nm laser was tuned to ionize atoms from the excited state prior to extraction in a static electric field. The electrons were detected on a phosphor screen attached to a micro channel plate charge amplifier.

2.2. Modelling a cold atom electron source

To model the CAES, we first assume the initial electron bunch has a Maxwellian momentum distribution described by
f(p)=(12πmkBT)3/2exp[|p|2+p||22mkBT]
(1)
where m is the electron mass, kB is the Boltzmann constant, T is the electron temperature, and the electron momentum is separated into a 2D component perpendicular to the propagation axis, p, and a component parallel to the propagation axis, p||. The transverse momentum spread σp=mkBT is small due to the very low electron temperature (Fig. 2), fundamentally limited by intrinsic heating processes immediately following ionization [17

17. J. L. Roberts, C. D. Fertig, M. J. Lim, and S. L. Rolston, “Electron temperature of ultracold plasmas,” Phys. Rev. Lett. 92, 253003 (2004). [CrossRef] [PubMed]

]. The electrons were accelerated along the propagation axis by electric field F, imparting an additional momentum component pF. Since pFp||, we regard the electron distribution as having a well-defined momentum component in this direction, such that the bunch is analogous to a quasi-monochromatic paraxial optical wavefield [18

18. W. H. Carter and E. Wolf, “Coherence and radiometry with quasihomogeneous planar sources,” J. Opt. Soc. Am. 67, 785 (1977). [CrossRef]

].

Fig. 2 Schematic of the quasi-homogeneous model as it applies to the cold atom electron source (left). Each electron has the same finite and uniform angular spread Δθ and hence angular distribution. Conventional sources (right) have a much larger associated angular spread with Δθ′ ≫ Δθ such that it is not possible to identify the origin of a detected electron.

The propagated electron bunch phase-space density for the transverse components, W(r,p), can therefore be described by
W(r,p)=f(p)I(r)
(2)
where I(r) describes the spatial intensity distribution of the source in the plane perpendicular to the propagation axis and Eq. (1) has been separated into transverse and parallel propagation components f (p) = f (p) f (p||) with
f(p)=f0exp(|p|22mkBT)
(3)
and f0 = 1/2πmkBT.

The quasi-homogeneous model (QHM) treats the source as a series of mutually incoherent point radiators each radiating into a small angular distribution (see Fig. 2). Conceptually, the effective source size at some point in the propagated electron beam is defined by the momentum spread (temperature) at the source, and not by the physical size of the source or electron beam. A QHM is appropriate for a source with short correlation length [16

16. K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99(99) (2010). [CrossRef]

], such as the CAES. The correlations in the field between two points r1 and r2 can then be described by the mutual optical intensity (MOI) for a quasi-homogeneous source
J(r,x)=I(r)γ(x)
(4)
where r = (r1 + r2)/2 and γ(x) describes the correlations between the electrons as a function of separation x = r1r2. The QHM naturally leads to the limit of a completely incoherent source by substituting a delta function for γ(x). The properties of quasi-homogeneous sources are discussed in detail in Refs. [16

16. K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99(99) (2010). [CrossRef]

, 18

18. W. H. Carter and E. Wolf, “Coherence and radiometry with quasihomogeneous planar sources,” J. Opt. Soc. Am. 67, 785 (1977). [CrossRef]

, 19

19. E. Wolf, “Coherence and radiometry,” J. Opt. Soc. Am. 68, 6–17 (1978). [CrossRef]

].

The standard methods of optical coherence theory may be adapted for the propagation of a partially coherent electron field. We make the paraxial approximation, and the intensity of the electron field at a distance z is then given by [16

16. K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99(99) (2010). [CrossRef]

]
I(r,z)=k24π2z2J(r,x)exp[ikzx(rr)]drdx
(7)
where k = 2π/λ and λ is the de Broglie wavelength of the electrons.

3. Measuring the spatial coherence function of a cold atom electron source

3.1. Arbitrarily shaped electron bunches

A unique feature of the CAES is that it allows virtual ‘masking’ of the electrons. We can alter the initial electron spatial distribution shot-to-shot by changing the SLM phase mask (see Fig. 1). The electron bunches can also be shaped along the propagation direction by control of the orthogonal photoionization laser beam profile [13

13. A. J. McCulloch, D. V. Sheludko, S. D. Saliba, S. C. Bell, M. Junker, K. A. Nugent, and R. E. Scholten, “Arbitrarily shaped high-coherence electron bunches from cold atoms,” Nat. Phys. 7, 785–788 (2011). [CrossRef]

]. This approach could be used to produce ‘pancake’ bunches that evolve naturally to form ideal uniform ellipsoidal density distributions to alleviate coherence loss due to non-linear Coulomb interactions within the bunch [14

14. O. J. Luiten, B. J. Claessens, S. B. van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, “Ultracold electron sources,” Int. J. Mod. Phys. A 22, 3882–3897 (2007). [CrossRef]

, 22

22. O. J. Luiten, S. B. van der Geer, M. J. de Loos, F. B. Kiewiet, and M. J. van der Wiel, “How to realize uniform three-dimensional ellipsoidal electron bunches,” Phys. Rev. Lett. 93, 094802 (2004). [CrossRef] [PubMed]

].

We impose a sinusoidal distribution on the cold atom cloud so that the MOI (Eq. (4)) becomes
J(r,x)=I02(1+sin(2πud))exp[|x|22lc2]
(8)
where d is the period of the sinusoid and r ≡ (u,v), so that
I(r,z)=k24π2z2I0(1+exp[λ2z2d2lc2]sin(2πud)).
(9)
The visibility measured at the detector, 𝒱 ≡ (ImaxImin)/(Imax + Imin), then reduces to
𝒱=exp[(1/d)2lc2/λ2z2].
(10)
Equation (9) describes a loss of visibility in a form that is mathematically identical to that obtained for a Young’s two-slit experiment in which the slits are placed in the source plane and the detector is sufficiently distant to produce the observed fringe frequency. This correspondence is not coincidental as can be seen when coherence is described in terms of the Wigner quasi-probability distribution (see, for example, Refs. [16

16. K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99(99) (2010). [CrossRef]

] and [23

23. M. A. Alonso, “Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles,” Adv. Opt. Photon. 3, 272–365 (2011). [CrossRef]

]). In both forms of the experiment, the coherence is determined from the visibility of the fringe pattern. In the form here, it is straightforward to vary the fringe spacing using the SLM and to probe the coherence function γ(x) at varying fringe frequencies, which is precisely equivalent to varying the slit separation.

3.2. Experimental method

The sinusoidal electron bunch signal incident on the MCP/phosphor screen was imaged with a CCD camera (Fig. 3). The images were integrated along v to improve the signal to noise ratio, and the line profiles were then normalized to an electron distribution without sinusoidal variation. Changes in the overall size of the electron bunch, caused by the inhomogeneous electric field at the accelerator aperture exit acting as a Davisson-Calbick lens [24

24. J. L. Hanssen, S. B. Hill, J. Orloff, and J. J. McClelland, “Magneto-optical-trap-based, high brightness ion source for use as a nanoscale probe,” Nano Lett. 8, 2844–2850 (2008). [CrossRef] [PubMed]

], do not affect the sinusoidal visibility. Figure 3 shows an example of a fit of Eq. (9) to a measured electron distribution for a single spatial frequency. The uncertainty in each visibility measurement was calculated using the error matrix from the non-linear least squares fit.

Fig. 3 (a) Desired excitation laser beam intensity profile used to create the spatial light modulator phase mask. (b) Image of resulting shaped electron bunch on the phosphor screen. (c) Integrated line profile of the calculated fully coherent electron distribution (red dashed), the recorded electron image (blue points), and a fit to the recorded data based on Eq. (9) (red solid).

3.3. Results

A Gaussian fit to the visibility as a function of spatial frequency, shown in Fig. 4, yields the transverse spatial coherence length, lc (Eq. (10)). The propagation distance z = 234 ± 15 mm is determined from a fit to electron and ion time of flight data and the electron de Broglie wavelength λ = 39 ± 1 pm is calculated from the imparted bunch energy. The resulting transverse coherence length is lc = 7.8 ± 0.9 nm with an inferred electron temperature of T = 14 ± 2 K. The coherence length measurement here is a lower limit as the reduction in visibility cannot be exclusively attributed to coherence effects. For example, a small distortion of the parallel sinusoidal pattern evident in Fig. 3 is due to non-uniform electric and magnetic fields during propagation [13

13. A. J. McCulloch, D. V. Sheludko, S. D. Saliba, S. C. Bell, M. Junker, K. A. Nugent, and R. E. Scholten, “Arbitrarily shaped high-coherence electron bunches from cold atoms,” Nat. Phys. 7, 785–788 (2011). [CrossRef]

].

Fig. 4 Visibility of electron bunch pattern as a function of spatial frequency, with a Gaussian fit to the visibility function resulting in lc = 7.8 ± 0.9 nm. The systematic uncertainty in measuring d was 3%.

Fig. 5 Variation of coherence length with excess ionization energy. The red dashed line shows how the coherence length varies with no additional disorder induced heating (T0 = 0K). The solid line is a least-squares fit to temperature-varying coherence length with heating of T0 = 9.9 ± 3 K.

4. Conclusion

Temperatures as low as T < 10±5 K have been measured for a CAES [13

13. A. J. McCulloch, D. V. Sheludko, S. D. Saliba, S. C. Bell, M. Junker, K. A. Nugent, and R. E. Scholten, “Arbitrarily shaped high-coherence electron bunches from cold atoms,” Nat. Phys. 7, 785–788 (2011). [CrossRef]

] indicating a characteristic coherence length of lc > 10 ± 3 nm. A coherence length of 10 nm is already sufficient at the source for imaging small biomolecules such as bacteriorhodopsin where the unit cell length is of order 10 nm. In contrast, photoemission electron sources with electron bunch temperatures of order T = 104 K have an associated coherence length of lc = 0.3 nm.

This paper has provided a framework for describing the propagation of partially coherent electron bunches extracted from a cold atom electron source: a critical requirement for realization of coherent diffractive imaging using a CAES. The arbitrary bunch shaping capability of the CAES has enabled a convenient and flexible method for measuring the transverse spatial coherence of the electron bunches. The measured coherence length of the CAES and the potential for high brightness are promising for application to coherent diffractive imaging of biological and other nanocrystals.

Acknowledgments

The authors acknowledge the support of the Australian Research Council through the Federation Fellowship program and ARC Discovery Project DP1096025.

References and links

1.

R. Henderson and P. N. T. Unwin, “Three-dimensional model of purple membrane obtained by electron microscopy,” Nature 257, 28–32 (1975). [CrossRef] [PubMed]

2.

B. G. Levi, “Focus on improving transmission electron microscopes starts to pay off,” Phys. Today 63, 15–19 (2010). [CrossRef]

3.

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, and A. H. Zewail, “Direct imaging of transient molecular structures with ultrafast diffraction,” Science 291, 458–463 (2001). [CrossRef] [PubMed]

4.

J. Cao, Z. Hao, H. Park, C. Tao, D. Kau, and L. Blaszczyk, “Femtosecond electron diffraction for direct measurement of ultrafast atomic motions,” Appl. Phys. Lett. 83, 1044 (2003). [CrossRef]

5.

B. J. Siwick, J. R. Dwyer, R. E. Jordan, and R. J. D. Miller, “An atomic-level view of melting using femtosecond electron diffraction,” Science 302, 1382–1385 (2003). [CrossRef] [PubMed]

6.

H. M. Quiney and K. A. Nugent, “Biomolecular imaging and electronic damage using X-ray free-electron lasers,” Nat. Phys. 7, 142–146 (2011). [CrossRef]

7.

2.M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, J.-M. Claverie, C. Bostedt, J. D. Bozek, S. Boutet, A. A. Miahnahri, M. Messerschmidt, J. Krzywinski, G. Williams, K. O. Hodgson, M. J. Bogan, C. Y. Hampton, R. G. Sierra, D. Starodub, I. Andersson, S. Bajt, M. Barthelmess, J. C. H. Spence, P. Fromme, U. Weierstall, R. Kirian, M. Hunter, R. Bruce Doak, Stefano Marchesini, Stefan P. Hau-Riege, Matthias Frank, Robert L. Shoeman, Lukas Lomb, Sascha W. Epp, Robert Hartmann, Daniel Rolles, A. Rudenko, C. Schmidt, L. Foucar, N. Kimmel, P. Holl, B. Rudek, B. Erk, A. Homke, C. Reich, D. Pietschner, G. Weidenspointner, L. Struder, G. Hauser, H. Gorke, J. Ullrich, I. Schlichting, S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K.-U. Kuhnel, R. Andritschke, C.-D. Schroter, F. Krasniqi, M. Bott, S. Schorb, Da. Rupp, M. Adolph, T. Gorkhover, H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, H. N. Chapman, and J. Hajdu, “Single mimivirus particles intercepted and imaged with an X-ray laser,” Nature 470, 78–81 (2011). [CrossRef] [PubMed]

8.

P. Piot, “Review of experimental results on high-brightness photo-emission electron sources,” in The Physics and Applications of High Brightness Electron Beams, J. Rosenzweig, ed. (World Scientific, 2003), pp. 127–142. [CrossRef]

9.

N. de Jonge, M. Allioux, J. T. Oostveen, K. B. Teo, and W. I. Milne, “Optical performance of carbon-nanotube electron sources,” Phys. Rev. Lett. 94, 186807 (2005). [CrossRef] [PubMed]

10.

T. van Oudheusden, P. L. E. M. Pasmans, S. B. van der Geer, M. J. de Loos, M. J. van der Wiel, and O. J. Luiten, “Compression of subrelativistic space-charge-dominated electron bunches for single-shot femtosecond electron diffraction,” Phys. Rev. Lett. 105, 264801 (2010). [CrossRef]

11.

B. J. Claessens, S. B. van der Geer, G. Taban, E. J. D. Vredenbregt, and O. J. Luiten, “Ultracold electron source,” Phys. Rev. Lett. 95, 164801 (2005). [CrossRef] [PubMed]

12.

S. B. van der Geer, M. J. de Loos, E. J. D. Vredenbregt, and O. J. Luiten, “Ultracold electron source for single-shot, ultrafast electron diffraction,” Microsc. Microanal. 15, 282 (2009). [CrossRef] [PubMed]

13.

A. J. McCulloch, D. V. Sheludko, S. D. Saliba, S. C. Bell, M. Junker, K. A. Nugent, and R. E. Scholten, “Arbitrarily shaped high-coherence electron bunches from cold atoms,” Nat. Phys. 7, 785–788 (2011). [CrossRef]

14.

O. J. Luiten, B. J. Claessens, S. B. van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, “Ultracold electron sources,” Int. J. Mod. Phys. A 22, 3882–3897 (2007). [CrossRef]

15.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, “Spatial coherence measurement of X-ray undulator radiation,” Opt. Commun. 195, 79–84 (2001). [CrossRef]

16.

K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99(99) (2010). [CrossRef]

17.

J. L. Roberts, C. D. Fertig, M. J. Lim, and S. L. Rolston, “Electron temperature of ultracold plasmas,” Phys. Rev. Lett. 92, 253003 (2004). [CrossRef] [PubMed]

18.

W. H. Carter and E. Wolf, “Coherence and radiometry with quasihomogeneous planar sources,” J. Opt. Soc. Am. 67, 785 (1977). [CrossRef]

19.

E. Wolf, “Coherence and radiometry,” J. Opt. Soc. Am. 68, 6–17 (1978). [CrossRef]

20.

J. J. Lin, D. Paterson, A. G. Peele, P. J. McMahon, C. T. Chantler, K. A. Nugent, B. Lai, N. Moldovan, Z. Cai, D. C. Mancini, and I. McNulty, “Measurement of the spatial coherence function of undulator radiation using a phase mask,” Phys. Rev. Lett. 90, 074801 (2003). [CrossRef] [PubMed]

21.

T. Gallagher, Rydberg Atoms (Cambridge University Press, 1994). [CrossRef]

22.

O. J. Luiten, S. B. van der Geer, M. J. de Loos, F. B. Kiewiet, and M. J. van der Wiel, “How to realize uniform three-dimensional ellipsoidal electron bunches,” Phys. Rev. Lett. 93, 094802 (2004). [CrossRef] [PubMed]

23.

M. A. Alonso, “Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles,” Adv. Opt. Photon. 3, 272–365 (2011). [CrossRef]

24.

J. L. Hanssen, S. B. Hill, J. Orloff, and J. J. McClelland, “Magneto-optical-trap-based, high brightness ion source for use as a nanoscale probe,” Nano Lett. 8, 2844–2850 (2008). [CrossRef] [PubMed]

25.

P. Gupta, S. Laha, C. E. Simien, H. Gao, J. Castro, T. C. Killian, and T. Pohl, “Electron-temperature evolution in expanding ultracold neutral plasmas,” Phys. Rev. Lett. 99, 075005 (2007). [CrossRef] [PubMed]

26.

R. Côté, T. Pattard, and M. Weidemüller, “Special issue on Rydberg physics,” J. Phys. B 38, (2005). [CrossRef]

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(030.1640) Coherence and statistical optics : Coherence
(110.4980) Imaging systems : Partial coherence in imaging
(140.3300) Lasers and laser optics : Laser beam shaping
(080.5084) Geometric optics : Phase space methods of analysis

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: January 10, 2012
Manuscript Accepted: January 25, 2012
Published: February 1, 2012

Citation
Sebastian D. Saliba, Corey T. Putkunz, David V. Sheludko, Andrew J. McCulloch, Keith A. Nugent, and Robert E. Scholten, "Spatial coherence of electron bunches extracted from an arbitrarily shaped cold atom electron source," Opt. Express 20, 3967-3974 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3967


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  23. M. A. Alonso, “Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles,” Adv. Opt. Photon.3, 272–365 (2011). [CrossRef]
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  25. P. Gupta, S. Laha, C. E. Simien, H. Gao, J. Castro, T. C. Killian, and T. Pohl, “Electron-temperature evolution in expanding ultracold neutral plasmas,” Phys. Rev. Lett.99, 075005 (2007). [CrossRef] [PubMed]
  26. R. Côté, T. Pattard, and M. Weidemüller, “Special issue on Rydberg physics,” J. Phys. B38, (2005). [CrossRef]

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