"Quantum efficiency" of photon detectors

Stephen Parrott

I am looking for a precise definition of "quantum efficiency"
of photon detectors, and also for information on how this is
measured in practice. The context is the following.

"Entangled" pairs of photons are generated by "parametric
downconversion". A laser beam is shined on a certain kind of crystal.
The crystal converts each absorbed photon into two photons,
traveling in different directions,
each with half the frequency (hence energy) of the absorbed photon.

The downconverted beams travel until they reach two spacelike
separated observers, traditionally called Alice and Bob. Alice and Bob
each have a photon detector which can detect a photon with polarization
"up" or "down", relative to an arbitrary direction
(which each can specify, independently). They set their detectors in
various directions and later get together to see if there was any
correlation between the polarizations of their detected photons.
Quantum mechanics predicts statistical correlations
which are classically impossible.

Alice <-------------- Crystal ---------------> Bob
|
|
|
Laser

A problem in interpreting this experiment is that the detectors
are typically inefficient, failing to detect some photons. Often,
Bob will detect a photon, but Alice will not detect hers. These are
called "singles" events, as opposed to "doubles", in which Alice and
Bob each detects a photon at the same time. Since correlation
of polarizations is meaningless for singles, they are
excluded from the data to be analyzed. The only meaningful data are
the doubles.

The quantum mechanical predictions assume perfect detectors.
But if we restrict our analysis to the doubles, how do we know that
our sample of doubles is statistically identical to the sample of
all photons? This is the so-called "fair sampling" or "detection"
loophole, which leaves open classical explanations for results
which would be classically impossible with perfect detectors.
Physicists have been trying to close this loophole
for about 50 years. It remains open, at least for the above
experiment with photons.

[A paper posted in the arXiv within the past month claims
to close the "detection loophole" in an experiment using
massive particles (ions) instead of photons. Are there any
experts out there willing to venture an opinion on its
significance? The reference is:

D.N. Matsukevich, P. Maunz, D.L. Moehring, S. Olmschenk, and
C. Monroe, "Bell inequality violation with two remote atomic
qubits", arXiv:0801.2184 [quant-ph] ]

Now for my questions. In analysis of such experiments,
the "quantum efficiency" of the detectors is often mentioned, but I
have never found a precise definition of this quantity in the literature.
How is it defined, and how is it measured in practice?

I can guess several plausible definitions, but I'm not sure
they are equivalent. I'm particularly interested in
the measurement question. In the above experiment, one plausible
definition of "quantum efficiency" calculates it with a formula
involving the ratio of singles to doubles.

Another plausible definition would be possible if there were a
way to determine the number of photons/sec in Alice's beam. Then one
could define the quantum efficiency as the ratio of the number
of photons/sec detected to the number of photons/sec present.
The interest of this would be that
it would determine the quantum efficiency independently of
knowing the ratio of singles to doubles. Then one could use the
observed ratio of singles to doubles as an experimental test to possibly
rule out a classical explanation for the results.
(If the quantum efficiency were *defined* as a function of the ratio of
singles to doubles, this would be circular.)

In principle, the number of photons/sec in Alice's beam could be
determined by calorimetric experiments because all the photons in the
beam have the same frequency, and hence the same energy via Planck's
formula.
From the heat produced by absorbing Alice's beam,
one could deduce the number of photons/sec.
But I have no idea if this might be experimentally possible. A recent
paper quotes 10,000 singles/sec in Alice's beam, corresponding to a
power of 5 x 10^(-8) ergs/sec. Is there any hope of measuring a heat/sec
this small?

While I'm writing, let me throw out another question.
In papers describing experiments like the above, I have seen
statements like: "The two-photon visiblity is 99%". What is the
precise meaning of "two-photon visibility" in this context?
This seems to be a different "visibility" than the quantity
generally mentioned in interference experiments (which measures
the "strength" of an interference pattern).

Tom Roberts

Stephen Parrott wrote:
> Now for my questions. In analysis of such experiments,
> the "quantum efficiency" of the detectors is often mentioned, but I
> have never found a precise definition of this quantity in the literature.
> How is it defined, and how is it measured in practice?

In high energy physics, we characterize photon detectors by quantum
efficiency, which is the probability of getting a signal given that a
photon of the appropriate wavelength is incident on the detector. A
typical photo-multiplier tube has a quantum efficiency around 20% -- so
for a blue photon incident on its photocathode, there is a 20%
probability that it will release a photoelectron that gets captured into
the dynode chain and generates a signal at the output (typical signals
are a few tens of millivolts into 50 Ohms). The manufacture typically
provides a graph of quantum efficiency as a function of photon wavelength.

A better photon detector is the Visible Light Photon Detector (VLPC),
which has a quantum efficiency around 80%. This is a glorified silicon
photodiode cooled to ~10K.

In HEP we usually want to detect charged particles, and do that by
coupling a scintillator to a photon detector. By designing the detector
to put 10 or more photons into the photodetector for a typical particle,
we get excellent overall efficiency, even with a mere 20% photon
efficiency. This does not apply to EPR-type experiments using photons,
of course.

Quantum efficiency can be measured by using a calibrated light source
attenuated down to a few thousand photons per second.


> In papers describing experiments like the above, I have seen
> statements like: "The two-photon visiblity is 99%". What is the
> precise meaning of "two-photon visibility" in this context?
> This seems to be a different "visibility" than the quantity
> generally mentioned in interference experiments (which measures
> the "strength" of an interference pattern).

I've not seen that term. But it seems related to efficiency.

To me, a two-photon efficiency of 99% for visible photons seems
unlikely. For N photons simultaneously incident on a detector with
quantum efficiency e, the overall detection probability with a
single-photon threshold is:
P(N) = 1 - (1-e)^N
For N=2 and e=.8, which is the best visible photon detector I know of,
that gives 96%. Note that for UV or higher-energy photons, higher
quantum efficiencies are possible, approaching 99% for few-MeV gammas.


Tom Roberts

Neil B.

"Stephen Parrott" <postnews@email.toast.net> wrote in message
news:47A6B0C2.1090003@email.toast.net...
...
> The downconverted beams travel until they reach two spacelike
> separated observers, traditionally called Alice and Bob. Alice and Bob
> each have a photon detector which can detect a photon with polarization
> "up" or "down", relative to an arbitrary direction
> (which each can specify, independently). They set their detectors in
> various directions and later get together to see if there was any
> correlation between the polarizations of their detected photons.
> Quantum mechanics predicts statistical correlations
> which are classically impossible.
>
> Alice <-------------- Crystal ---------------> Bob
> |
> |
> |
> Laser
>
> A problem in interpreting this experiment is that the detectors
> are typically inefficient, failing to detect some photons. Often,
> Bob will detect a photon, but Alice will not detect hers. These are
> called "singles" events, as opposed to "doubles", in which Alice and
> Bob each detects a photon at the same time. Since correlation
> of polarizations is meaningless for singles, they are
> excluded from the data to be analyzed. The only meaningful data are
> the doubles.
>
> The quantum mechanical predictions assume perfect detectors.
> But if we restrict our analysis to the doubles, how do we know that
> our sample of doubles is statistically identical to the sample of
> all photons? This is the so-called "fair sampling" or "detection"
> loophole, which leaves open classical explanations for results
> which would be classically impossible with perfect detectors.
> Physicists have been trying to close this loophole
> for about 50 years. It remains open, at least for the above
> experiment with photons.
...

I have long wondered how unreliable detectors affect the "collapse of the
wave function." Discussions of QM measurement assume perfect detection,
which then must collapse the WF since it can't be elsewhere. But what if the
detector misfires or fails to detect, then what "happens" to the wave? We
don't even know when or if this happened, despite the concept of "knowledge"
being presumed critical to measurement in QM.

It reminds me of the Renninger negative measurement, where failure to detect
the particle (in a case where the detector is reliable) means that the
particle must be elsewhere - that is a case of "reallocation" rather than
"collapse" of the WF.

Stephen Parrott

Tom Roberts wrote:
> Stephen Parrott wrote:
>> Now for my questions. In analysis of such experiments,
>> the "quantum efficiency" of the detectors is often mentioned, but I
>> have never found a precise definition of this quantity in the literature.
>> How is it defined, and how is it measured in practice?
>
> In high energy physics, we characterize photon detectors by quantum
> efficiency, which is the probability of getting a signal given that a
> photon of the appropriate wavelength is incident on the detector. A
> typical photo-multiplier tube has a quantum efficiency around 20% -- so
> for a blue photon incident on its photocathode, there is a 20%
> probability that it will release a photoelectron that gets captured into
> the dynode chain and generates a signal at the output (typical signals
> are a few tens of millivolts into 50 Ohms). The manufacture typically
> provides a graph of quantum efficiency as a function of photon wavelength.

Thank you. That's all very helpful, though it doesn't entirely answer
my questions.

As you say, the idea of "quantum efficiency" seems to be the ratio
of photons detected to photons received. But I still am not clear
on how one measures photons received. I don't see how that could
be done unless one had a detector with 100% efficiency,
or at least a precisely known efficiency, or some independent method
which relates number of photons to some other measurable quantity such
as energy.

>
>> In papers describing experiments like the above, I have seen
>> statements like: "The two-photon visiblity is 99%". What is the
>> precise meaning of "two-photon visibility" in this context?
>> This seems to be a different "visibility" than the quantity
>> generally mentioned in interference experiments (which measures
>> the "strength" of an interference pattern).
>
> I've not seen that term. But it seems related to efficiency.
>
> To me, a two-photon efficiency of 99% for visible photons seems
> unlikely. For N photons simultaneously incident on a detector with
> quantum efficiency e, the overall detection probability with a
> single-photon threshold is:
> P(N) = 1 - (1-e)^N
> For N=2 and e=.8, which is the best visible photon detector I know of,
> that gives 96%. Note that for UV or higher-energy photons, higher
> quantum efficiencies are possible, approaching 99% for few-MeV gammas.

A typical statement of that type is the following, from
"An experimental test of non-local realism" by S. Groeblacher, et. al.,
Nature 446 (2007), 871-875, arXiv:0704.2529v1 [quant-ph].
At the bottom of p. 5 (arXiv version) they write:

"The two-photon visibilities are approximately 99.0 +- 1.2%...
which - to our knowledge - is the highest reported visibility
for a pulsed SPDC scheme."

Their photons have wavelength 395 nm, which is on the border between
visible blue light and low-energy ultraviolet.

Thomas Smid

[To the moderator (please remove before posting): this is a re-edit of
the post I submitted yesterday. Please ignore the previous submission
and post only this one if possible. Thanks.]

On 5 Feb, 11:04, Stephen Parrott <postn...@email.toast.net> wrote:
> I am looking for a precise definition of "quantum efficiency"
> of photon detectors, and also for information on how this is
> measured in practice. The context is the following.
>
> "Entangled" pairs of photons are generated by "parametric
> downconversion". A laser beam is shined on a certain kind of crystal.
> The crystal converts each absorbed photon into two photons,
> traveling in different directions,
> each with half the frequency (hence energy) of the absorbed photon.
>
> The downconverted beams travel until they reach two spacelike
> separated observers, traditionally called Alice and Bob. Alice and Bob
> each have a photon detector which can detect a photon with polarization
> "up" or "down", relative to an arbitrary direction
> (which each can specify, independently). They set their detectors in
> various directions and later get together to see if there was any
> correlation between the polarizations of their detected photons.
> Quantum mechanics predicts statistical correlations
> which are classically impossible.
>
> Alice <-------------- Crystal ---------------> Bob
> |
> |
> |
> Laser
>
> A problem in interpreting this experiment is that the detectors
> are typically inefficient, failing to detect some photons. Often,
> Bob will detect a photon, but Alice will not detect hers. These are
> called "singles" events, as opposed to "doubles", in which Alice and
> Bob each detects a photon at the same time. Since correlation
> of polarizations is meaningless for singles, they are
> excluded from the data to be analyzed. The only meaningful data are
> the doubles.
>
> The quantum mechanical predictions assume perfect detectors.
> But if we restrict our analysis to the doubles, how do we know that
> our sample of doubles is statistically identical to the sample of
> all photons? This is the so-called "fair sampling" or "detection"
> loophole, which leaves open classical explanations for results
> which would be classically impossible with perfect detectors.
> Physicists have been trying to close this loophole
> for about 50 years. It remains open, at least for the above
> experiment with photons.

> Now for my questions. In analysis of such experiments,
> the "quantum efficiency" of the detectors is often mentioned, but I
> have never found a precise definition of this quantity in the literature.
> How is it defined, and how is it measured in practice?

The single count rate is given by

(1) N1=e1*A ,

where A is the activity of the source (decays/sec) and e1 the overall
detection efficiency for channel 1 (which not only includes the
quantum efficiency of the detector, but also a transmission efficiency
due to losses in the optics, and a geometrical factor (associated with
the assumption of the photons being discrete particles and the
detector only having a finite size)).
So assuming statistical independence, the coincidence (double) count
rate is then

(2) N1,2=e1*e2*A ,

where e2 is the corresponding efficiency for channel 2 . And if you
now take the ratio N1,2/N1=e2 and correspondingly N1,2/N2=e1, you
know the overall detection efficiencies. This is, as far as I am
aware, the only practical way to do it, because usually you don't
know the activity A for sure (which in this way drops out). However,
there is a potential flaw with Eq.(2): the point is that if you have
correlated emissions (like in these kind of experiments), one would
have to assume (because of angular momentum conservation) that the two
photons are emitted exactly into opposite directions, i.e. (assuming
the experiment is properly aligned) photon 2 should reach the detector
whenever photon 1 reaches the detector; in other words, the
geometrical efficiency is not statistically independent anymore, so
if in general you have e1=e1_g*e1_q and e2=e2_g*e2_q (neglecting
transmissive losses) , you would have here e2_g=1, and thus the
coincidence count rate would be

(3) N1,2 = e1_g*e1_q*1*e2_q*A

rather than

(4) N1,2 = e1_g*e1_q*e2_g*e2_q*A

as for the statistically independent case (which is usually assumed
here).

This means that

(5) N1,2/N1= e2_q

instead of

(6) N1,2/N1= e2_g*e2_q .

But if one assumes a typical quantum efficiency e2_q=0.2 , Eq.(5)
(which should apply for correlated emissions) would not be consistent
with observations at all, as typically N1,2/N1=10^-3.

This circumstance (and some others as well) has actually led me to
formulate a theory for the photodetection process (see
http://www.plasmaphysics.org.uk/photoionization.htm ) which not only
could explain this discrepancy, but indeed also the outcome of the
Bell test experiments in terms of semi-classical physics (at least as
far as those involving light are concerned). In a nutshell: for
crossed polarizers, the electromagnetic field in the two channels is
anti-correlated (rather than correlated as for parallel polarizers)
and this leads only to a very small probability of simultaneous
photodetection considering the statistical nature of the process; see
http://www.physicsmyths.org.uk/bell.htm for more).

> While I'm writing, let me throw out another question.
> In papers describing experiments like the above, I have seen
> statements like: "The two-photon visiblity is 99%". What is the
> precise meaning of "two-photon visibility" in this context?
> This seems to be a different "visibility" than the quantity
> generally mentioned in interference experiments (which measures
> the "strength" of an interference pattern).

As I understand it, 'visibility' is defined here as (N1,2_max-
N1,2_min)/(N1,2_max+N1,2_min) , where N1,2_max is the coincidence
count rate for parallel polarizers, and N12_min for crossed
polarizers.

> [A paper posted in the arXiv within the past month claims
> to close the "detection loophole" in an experiment using
> massive particles (ions) instead of photons. Are there any
> experts out there willing to venture an opinion on its
> significance? The reference is:
>
> D.N. Matsukevich, P. Maunz, D.L. Moehring, S. Olmschenk, and
> C. Monroe, "Bell inequality violation with two remote atomic
> qubits", arXiv:0801.2184 [quant-ph] ]

This experiment apparently still involved coincidence detection of
photons, and thus the issues associated with the photodetection
process remain.

Thomas