Table Of ContentElectron matter wave interferences at high vacuum pressures
G. Schu¨tz1, A. Rembold1, A. Pooch1, W.T. Chang2 and A. Stibor1,
∗
1Institute of Physics and Center for Collective Quantum Phenomena in LISA+,
University of Tu¨bingen, Auf der Morgenstelle 15, 72076 Tu¨bingen, Germany
2Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan, Republic of China
The ability to trap and guide coherent electrons is gaining importance in fundamental as well
as in applied physics. In this regard novel quantum devices are currently developed that may
operateunderlowvacuumconditions. Herewestudythelossofelectroncoherencewithincreasing
background gas pressure. Thereby, optionally helium, hydrogen or nitrogen is introduced in a
biprisminterferometerwheretheinterferencecontrastisameasureforthecoherenceoftheelectrons.
The results indicate a constant contrast that is not decreasing in the examined pressure range
between10−9mbarand10−4mbar. Therefore,nodecoherencewasobservedevenunderpoorvacuum
5 conditions. Due to scattering of the electron beam with background H -molecules a signal loss of
2
1 94% was determined. The results may lower the vacuum requirements for novel quantum devices
0 with free coherent electrons.
2
r
p I. INTRODUCTION background gas pressure. The gradual loss of coherence
A through collisions with background gases was analyzed
4 The coherent control and interference of free electrons for neutral C60-fullerenes in a near field Talbot-Lau
matter wave interferometer [14]. Thereby, decoherence
1 has a long history. In the 1950s a mayor scientific break-
was observed at a gas pressure of ∼ 10 6mbar.
through happened with the development of biprism −
] electron interferometers [1]. A variety of experiments
h In this work we study the possible loss of coherence for
for free electrons were accomplished in the following
p electron matter waves in a biprism interferometer in
- decades proving e.g. the magnetic Aharonov-Bohm
t effect [2], the Sagnac effect [3] or Hanbury Brown-Twiss presence of helium (He), nitrogen (N2) or hydrogen (H2)
n
background gas. Our instrument is able to generate
a anticorrelations [4]. In recent years the coherent con-
interferograms with high interference contrast in a
u trol of free electrons is gaining again importance for
q fundamental research and in a technical point of view. pressure range between 10−9 and 10−4mbar. It is only
[ limitedbythevacuumspecificationsofthemultichannel
This can be observed in decoherence studies of electrons
plate (MCP) detector. We will demonstrate that in this
4 near semiconducting surfaces [5] and developments such
whole pressure region no decoherence can be observed.
v as a field emission source for free electron femtosecond
4 pulses [6, 7], surface-electrode chips [8] or a biprism
3
electron interferometer with a single atom tip source [9].
6 II. SETUP
New quantum devices with coherent electrons are cur-
5
rently implemented like a recently proposed noninvasive
0
. quantum electron microscope [10]. Due to the quantum A scheme of our experimental setup is shown in Fig. 1
1 Zeno effect it potentially reduces the electron radiation and is described in detail elsewhere [9, 15–17]. In our
0
exposure during scanning of fragile biological samples approachtheelectronbeamisfieldemittedbyanetched
5
by two orders of magnitude. tungsten tip that is covered with a monolayer of irid-
1
ium and annealed to form a protrusion in the nanometer
:
v Some of these applications may operate under low regime [18, 19]. The tip forming procedure is monitored
i
X vacuum conditions or are technically less demanding to by a MCP-detector that can be moved out of the opti-
r realize if an ultra-high vacuum (UHV) environment is cal axis. The electrons start with an emission energy of
a not needed. The question arises, how background gases 1.58keV for the experiment with He and N2 background
influence the properties of the matter wave. Important gas and 1.44keV for the one with H2. They coherently
applications such as reflection high energy electron illuminate a 400nm wide gold covered biprism fiber that
diffraction (RHEED) for in situ monitoring of the divides and combines the electron matter waves [1, 9].
growth of thin films on surfaces [11] or ultrafast electron It is set on a positive potential of 0.35V for the experi-
diffraction (UED) at molecular beams for direct imaging ments with He or N2 background gas and 0.4V for H2.
of transient molecular structures [12, 13] are known to All beam alignment is performed by electrostatic deflec-
work at high background gas pressures. tion electrodes. Behind the biprism the partial waves
However, it has not been studied yet, how the coher- overlap and interfere with each other. The interference
ence of an electron beam is influenced by increasing pattern has a period of several 100nm and is oriented
parallel to the biprism in the x-direction. It is magnified
by an electrostatic quadrupole lens to fit the detectors
resolution of about 100µm. The image rotator, a mag-
∗Electronicaddress: [email protected] netic coil, allows to rotate the interferogram to correct
2
FIG.1: (Coloronline)Experimentalsetupofthebiprisminterferometertotesttheelectroncoherenceforincreasingbackground
gas pressure (not to scale) [9, 15–17].
III. MEASUREMENTS
60
Three experimental runs were performed introducing ei-
ther He, N or H gas in the UHV chamber. Before each
2 2
)
% run, the tip was annealed to form a protrusion being the
( emission center. Therefore, possible variations in the tip
K 40
apex size influencing the electron emission voltage and
t
as themaximalcontrastcannotberuledout. Themeasure-
r
t ment started at a background gas pressure of 10 9mbar
n −
co 20 and electron interferograms were recorded with a signal
acquisitiontimeof25sforHeorN and22sforH . Then
2 2
He a further small amount of gas was introduced through
N2 the nozzle. At equilibrium another interference pattern
0 was recorded. This process was repeated stepwise with
10−8 10−7 10−6 increasing pressure for the different gases. Background
gas pressure (mbar) images for the same integration time were acquired in
the experiments with He or N by switching off the field
2
emission subsequently to each recording. This data was
FIG. 2: (Color online) Electron interference contrast K as a
subtractedfromtheinterferograms. FortheH measure-
function of increasing pressure of helium (He, blue squares) 2
or nitrogen (N , red dots) background gas. ment no background subtraction was necessary since the
2
ion getter pump, as the main source of background, was
turnedoff. Therecordedimageswereanalyzedbyadding
all counts in the pixel-rows of the detector along the x-
directionoftheinterferencepatternanddividingthesum
possible misalignments. The interference pattern is de- by the amount of pixel-columns. The distribution of the
tected by a MCP-detector with a delay line anode. It is resulting average interference pattern I(y) versus the y-
able to operate at background gas pressures up to about direction normal to the interference stripes was fitted by
10−4mbar. Above that level the risk of destruction of the following expression to determine the mean intensity
the MCPs due to electric discharges is high. I , the pattern periodicity d and the contrast K [22]
0 s
(cid:20) (cid:18) (cid:19)(cid:21)
The whole interferometer has a length (tip to detector) 2πy
I(y)=I 1+Kcos . (1)
of 565mm. It is constructed rigidly [20] to avoid me- 0 d
s
chanical vibrations and shielded against electromagnetic
noise [21] by a copper and mu-metal tube. The inlet of In Fig. 2 the resulting contrast is plotted versus the
different background gases is performed by an UHV gas background gas pressure for He and N . The contrast
2
nozzle. The interferometer is placed in a chamber where distribution is rather constant for the whole measured
a minimum pressure of 1×10 10mbar is achieved by an pressure range indicating the electrons remain coher-
−
ion getter pump in combination with a cryopump. ent. At higher pressures the ion pump produced an
3
80
1.5
u.]
60 a.
[
%) 12 I0
( 10 y 1
astK 40 n[mm] 5 8 tensit
contr directio 0 4 eanin0.5
20 y−5 m
0
0 4 8
xdirection[mm]
0
0 10 8 10 7 10 6 10 5 10 4
10 8 10 7 10 6 10 5 10 4 − − − − −
− − − − −
H pressure (mbar)
H pressure (mbar) 2
2
FIG.4: Meanelectronintensityonthedetectorasafunction
FIG. 3: (Color online) Electron interference contrast K as a
of increasing pressure of H background gas.
function of increasing pressure of hydrogen (H ) background 2
2
gas. Inset: ElectroninterferencepatternataH gaspressure
2
of 7.3 × 10−9mbar.
contrast. In our far field interferometer the situation is
different. After a collision with a significantly heavier
increasing noise level of ions on the detector that leads background gas atom or molecule, the electron is in
to greater error bars and a higher dispersion of the data most cases scattered into an angle large enough to miss
points. For hydrogen we were able to work without the detector. Due to the quadrupole magnification,
the ion getter pump and stabilized the pressure only minimal deflection of the electrons trajectory lead to
with the cryopump. This significantly reduced the a large displacement in the detection plane. This is
backgroundcountsresultinginamorestablesignal. The indicatedbythesignificantsignallossof94%comparing
pressure-dependent contrast for hydrogen is shown in the mean electron intensity measured on the detector
Fig.3. Itisconstantaround67%. Theinsetillustratesa at a H pressure of 7.3 × 10 9mbar with the one at
2 −
typicalinterferencepatternrecordedat7.3 × 10−9mbar. 9.3 × 10−5mbar. In other words, those electrons that
made it to the detector did not scatter on a gas atom
Additionally, the mean intensity I0 of the interference and are therefore still coherent. It is an advantage of
pattern on the detector was determined for hydrogen thissetuptobeabletoselecttheseelectronsandremain
with increasing pressure. It represents the center line high contrast interference pattern even under rather low
of the cosine-function in Eq. 1. The data is plotted vacuum conditions.
in Fig. 4. As expected, a significant signal drop is
determined. This is presumably due to increasing Due to possible electric discharges in the MCP-
collisions between electrons and H2 molecules that detector, interference at even higher vacuum pressures
decreasethecountrate. Atapressureof9.3×10−5mbar could not be studied. However, coherent behaviour of
onlyafractionof6%oftheoriginalelectronsignalisleft. electrons at a comparable pressure of ∼ 3×10 4mbar
−
was reported in an UED experiment [12] and for sig-
nificantly higher pressures in a RHEED measurement
[11]. The latter describes electron diffraction on SrTiO
3
IV. DISCUSSION AND CONCLUSION and YBa Cu O surfaces at an oxygen background
2 3 7 δ
pressure up to 0−.15mbar. This was possible due to
We have studied the coherent properties of electron a short design of the setup, a differential pumping
matter waves in a biprism interferometer under low unit for the source and significantly higher electron
vacuum conditions by introducing helium, nitrogen or energies of 35keV that allowed to work without MCP
hydrogen background gas in the UHV chamber. Unlike amplification prior to the detection on the fluorescent
to interference experiments with C fullerenes [14] the screen. In accordance to our observations, also a strong
60
electrons in our instrument do not show decoherence up scattering loss of electrons in the high oxygen pressure
to a pressure of ∼ 10 4mbar which can be observed in was observed in the RHEED experiment [11].
−
a constant interference contrast. In the C near field We therefore conclude that with different detection
60
interferometer the heavy molecules have a significant methods and shorter configurations, electron diffraction
probability to be measured in the region between the or interference may be observed at even higher back-
interference stripes after a collision, leading to a loss of ground gas pressures. The results of our experiments
4
provide an indication of the vacuum requirements for through the Emmy Noether program STI 615/1-1. A.R.
novel devices applying free coherent electrons. acknowledges support from the Evangelisches Studien-
werk e.V. Villigst.
V. ACKNOWLEDGEMENTS
This work was supported by the Deutsche Forschungs-
gemeinschaft (DFG, German Research Foundation)
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