Detecting noise with shot noise using on-chip photon detector
Transcript Of Detecting noise with shot noise using on-chip photon detector
This is a repository copy of Detecting noise with shot noise using on-chip photon detector. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/87856/ Version: Accepted Version Article: Jompol, Y., Roulleau, P., Jullien, T. et al. (4 more authors) (2015) Detecting noise with shot noise using on-chip photon detector. Nature Communications, 6. 6130. ISSN 2041-1723 https://doi.org/10.1038/ncomms7130
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Detecting noise with shot noise: a new on-chip photon detector
Y. Jompol1,∗,†, P. Roulleau1,∗, T. Jullien1, B. Roche1, I. Farrer2, D.A. Ritchie2, and D. C. Glattli1
1Nanoelectronics Group, Service de Physique de l’Etat Condense, IRAMIS/DSM (CNRS URA 2464), CEA Saclay, F-91191 Gif-sur-Yvette, France 2Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, UK
1
The high frequency radiation emitted by a quantum conductor presents a rising interest in quantum physics and condensed matter[1, 6, 3, 4, 5, 7, 8]. However its detection with microwave circuits is challenging. The important mismatch between the quantum conductor impedance (∼ h/e2) and the circuit impedance (typically 50 Ω) strongly limits the sensitivity. Recent realization of on-chip quantum detection [7, 9, 10, 11, 12, 13] have circumvented this issue using spatially close detectors with larger impedance providing high sensitivity up to high frequency. However, they lack of a universal photon-response. Here, we propose to use the PhotonAssisted Shot Noise (PASN) for on-chip radiation detection. It is based on the low frequency current noise generated by the partitioning of photon excited electrons and holes which are scattered inside the conductor [14, 15, 16, 17]. For a given electromagnetic coupling to the radiation, the PASN response is independent on the nature and geometry of the quantum conductor used for the detection, up to a Fano factor, characterizing the type of scattering mechanism. Ordered in temperature/frequency range, from few tens of milli-Kelvin/GHz to several hundreds of Kelvin/THz, a wide variety of conductors can be used like Quantum Point Contacts (this work), diffusive metallic or semi-conducting films, Graphene, Carbon nanotubes and even molecule, opening new experimental opportunities in quantum physics.
2
To circumvent impedance mismatch limitation, different types of on-chip photon detectors have been developed using a second nearby quantum conductor and exploiting its photon detection ability. On-chip detectors have been realized using GaAs/AlGaAs 2D electron gas patterned quantum dots [9, 10] and Aluminium or Niobium SIS junctions [11, 12, 13, 7]. The photonresponse of quantum dots depends on an energy scale set by their geometry, that of superconducting junctions is limited by a characteristic energy gap and both systems show tunnel resistance variability. Regarding bolometric detectors their efficiency depends on the phonon relaxation time, requires low temperature and shows slow response time.
In this letter, we propose a novel on-chip radiation detection based on PASN. When a quantum conductor is submitted to a time dependent drainsource voltage, electrons and holes are created which then scatter inside the conductor. Their partitioning between source and drain contacts leads to a current noise called Photo-Assisted Shot Noise. Remarkably, there is a simple link between PASN and the incident radiation power up to a noise Fano factor characterizing the statistics of partitioning. This simple link is better understood if we remark that PASN is the quantum manifestation of the rectification property of ordinary shot noise [18, 19, 20, 21] which is proportional to the absolute value of the drain-source voltage.
Figure 1 shows the principle of the on-chip detection. It consists of two separate excitation and measurement circuit lines etched in a high mobility two-dimensional electron gas (2DEG). Each line involves two QPCs in se-
3
ries. On the upper line, the left QPC is the high-frequency emitter. When
biased by the dc voltage VdEs it generates shot noise up to the frequency eVdEs /h [20, 22]. The right QPC tuned on a conductance plateau acts as a stable series resistance RSE converting current noise into voltage noise. In
the lower line the left QPC is the detector. In series with the right QPC,
also tuned on a resistance plateau RSD, it experiences the emitter line volt-
age fluctuations via the coupling capacitance CC up to the cut-off frequency
fmax [23]. The number of electron-hole pairs generated in the detector line
is a direct function of the radiated noise power integrated up to frequency
m
i
n
(
e
V
E ds
/
h
,
f
m
a
x
)
.
Their scattering by the QPC detector generates a low-
frequency PASN which is measured. fmax depends on all QPC resistances
and on the self-capacitance Cself of the 2DEG part between the QPCs in
series.
To understand the photon detection principle, let us first assume that the
detector line is excited by a coherent radiation at frequency Ω/2π such that
VdEs (t) = Vac cos(Ωt). Electrons in the detector line can absorb l photons of
energy El=l Ω by creating an electron-hole pair with a probability P (El)=
| Jl(eVac/ Ω) |2, with Jl the lth Bessel function. Electrons and holes are
independently and randomly partitioned by the QPC detector between left
and right contacts. This generates a PASN whose low-frequency spectral
density of current fluctuations SIP ASN is given by [14, 15, 16, 17]:
4
SP ASN
2e2 = [4kBTe
D2 +
I
h
D,n
n
l=+∞
El
2 DD,n(1 − DD,n)
ElP (El) coth 2kBTe ]
(1)
n
l=−∞
with Te the electronic temperature and DD,n the transmission of the nth electronic mode through the detector QPC, n=1, 2, ... . For weak ac voltage eVac ≪ Ω and zero temperature a direct relation can be established between the radiation power Prad = Va2c/2Zrad and the current noise: SIP ASN ≃ 2GDF (Zrade2/ )Prad/Ω, where Zrad is the radiation impedance assumed smaller than the QPC detector conductance GD and F the Fano factor.
From Eq. (1), it is clear that the maximum PASN will be obtained for total transmission DD = n DD,n = k + 1/2, k an integer. In addition to shot noise, a photon assisted dc current Iph is generated when considering the (weak) energy dependence of the QPC transmission :
I = 2e dǫ(− ∂f )( ∂DD,n ) l=+∞ E2P (E )
(2)
ph h
∂ǫ
∂ǫ
l
l
n
l=−∞
f (ǫ) is the equilibrium Fermi distribution. Modeling the QPC transmission with a saddle point potential [24, 25], it can be shown that ∂D∂Dǫ ,n ∝ DD,n(1−DD,n): maximum photocurrents will be also obtained at half-integer
DD.
5
In the present case, the excitation is not coherent but due to random fluctuations of the QPC detector drain-source voltage which originates from the capacitive coupling with the noisy QPC emitter. The above expressions can be generalized, giving the PASN as:
SP ASN
2e2 = [4kBTe
D2 +
I
h
D,n
n
E
2 DD,n(1 − DD,n) EP (E) coth 2kBTe dE]
(3)
n
and the photocurrent:
Iph = 2e dǫ(− ∂f )( ∂DD,n ) E2P (E)dE
(4)
h ∂ǫ n ∂ǫ
The generalized probability distribution P (E) is similar to the P (E) function
used in the dynamical Coulomb blockade theory (see Supplementary Infor-
mation). It is a direct function of the radiation power to be detected, which
as a shot noise itself is maximum for DE = 0.5.
We first focus on the photocurrent whose measurement set-up is described
in Fig. 2(a). Source Vin leads to a current in the upper line and to the
voltage difference VdEs across the emitter. The resulting shot noise induces
a photocurrent Iph in the detector. We modulate Vin at frequency 174 Hz
and detect the induced photocurrent using lock-in techniques. Series resis-
tances are tuned on a plateau for each line while the emitter and detector
6
transmissions are varied. Following the saddle point potential model of a QPC [24, 25], the transmission of the nth mode can be written DD,n(Vg) = 1/(1+e2π(V0−Vg)/Vg,n) where Vg,n is related to the negative curvature of the saddle point potential. The photocurrent is given by (see Supplementary Information):
Iph = e 1 kBTE∗ e2
2π DD,n(1 − DD,n)
(5)
h ∆ Cself n Vg,n
Vg,n and the lever arm ∆ = ∂ǫ/∂Vg are extracted from a study of the differential QPC conductance versus gate and bias voltages. We have introduced TE∗ as the effective noise temperature of the circuit which, up to a coupling factor, includes a combination of the shot noise temperature of the emitter: (1 − DE) e2VkdBEs plus other equilibrium thermal noise contributions of the circuit surrounding the detector QPC (see the supplementary Information).
The color plot in Fig. 2(b) shows the measured photocurrent as a function of the emitter and detector transmissions DE and DD, up to two transmitting orbital electronic modes. Above the color plot, the photocurrent is plotted as a function of DD for a fixed value of DE ∼ 0.45. As expected, it is maximum for half transmission of the emitter electronic modes and vanishes for integer transmission. These measurements have been found essential for a fine calibration of the electrical circuit and for complementary characterization of the photon-assisted shot noise effect (see the Supplementary Information).
7
We now consider PASN measurements. The cross correlation noise measurement set up is described in Fig. 3(a). To characterize the detector line, the QPC detector transmission is set to DD = 0.5 while a dc bias is applied on the detector line. The resulting shot noise measured, black dots in Fig. 3(b), perfectly agrees with the theory in red solid line. We extract an electronic temperature Te = 310 mK close to the fridge temperature T = 300 mK . Then we turn off the applied bias on the detector line and the QPC emitter is biased and also tuned at transmission DE = 0.5. Both series resistances are tuned on the first plateau. Because of the coupling capacitance, voltage fluctuations are reported on the detector line. The only dc current flowing through the detector line being the weak dc photocurrent, no detectable transport shot noise is expected. However, we detect some noise, confirming that the PASN detection works as illustrated in Fig. 3(c), black circle. The detected PASN, ∆SIP ASN,D, is expected to be:
∆SP ASN,D
≃
4e2 − DD(1
−
DD)
e2
TE∗
(6)
I
h
Cself 6Te
Here, considering P (E) takes only important values for E ≪ kBTe, a lowenergy expansion of Eq. (3) has been made. The TE∗ (VdEs )/Cself amplitude compatible with the detector geometry (estimated Cself =3 fF and Cc=1 fF) and obtained from photocurrent measurements can now be compared to the noise measurement. The theoretical prediction (red solid line) following Eq. 6 also includes an additional term due to heating effect. We discuss this
8
point in the following.
We open the series QPC of the detector line such that the current to voltage fluctuation conversion is now mediated by the smaller resistance of the long resistive mesa. Then we apply a fixed bias VdDs and sweep the detector transmission (red circles in Fig. 4(a)). As expected the shot noise is maximum for DD = 0.5 and cancels for DD = 1. The slight disagreement with the theoretical prediction (red solid line) around DD ∼ 0.7 reveals a weak ”0.7” anomaly [26, 27, 28, 29]. Then we tune the series QPC on its first plateau and repeat the same experiment (black circles). Surprisingly, the shot noise does not cancel anymore for DD = 1. To understand it, we must consider heating effects. Since the size of the QPC is much smaller than the electron-phonon relaxation length, there is a temperature gradient from the QPC to the ohmic contacts assumed to be at the base temperature of the fridge. Combining Joule heating together with the Wiedemann-Franz law, we obtain [18]:
Te(Vds) = T 2 + 24 G (1 + 2G )( eVds )2
(7)
fridge π2 Gm
Gm 2kB
with Gm the total conductance linking the QPC to the ohmic contacts, and Tfridge the base temperature. Considering this effect, a QPC tuned on a plateau will not be noiseless anymore. We find a good agreement with measurements, black solid line.
9
Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request.
[email protected] https://eprints.whiterose.ac.uk/
Detecting noise with shot noise: a new on-chip photon detector
Y. Jompol1,∗,†, P. Roulleau1,∗, T. Jullien1, B. Roche1, I. Farrer2, D.A. Ritchie2, and D. C. Glattli1
1Nanoelectronics Group, Service de Physique de l’Etat Condense, IRAMIS/DSM (CNRS URA 2464), CEA Saclay, F-91191 Gif-sur-Yvette, France 2Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, UK
1
The high frequency radiation emitted by a quantum conductor presents a rising interest in quantum physics and condensed matter[1, 6, 3, 4, 5, 7, 8]. However its detection with microwave circuits is challenging. The important mismatch between the quantum conductor impedance (∼ h/e2) and the circuit impedance (typically 50 Ω) strongly limits the sensitivity. Recent realization of on-chip quantum detection [7, 9, 10, 11, 12, 13] have circumvented this issue using spatially close detectors with larger impedance providing high sensitivity up to high frequency. However, they lack of a universal photon-response. Here, we propose to use the PhotonAssisted Shot Noise (PASN) for on-chip radiation detection. It is based on the low frequency current noise generated by the partitioning of photon excited electrons and holes which are scattered inside the conductor [14, 15, 16, 17]. For a given electromagnetic coupling to the radiation, the PASN response is independent on the nature and geometry of the quantum conductor used for the detection, up to a Fano factor, characterizing the type of scattering mechanism. Ordered in temperature/frequency range, from few tens of milli-Kelvin/GHz to several hundreds of Kelvin/THz, a wide variety of conductors can be used like Quantum Point Contacts (this work), diffusive metallic or semi-conducting films, Graphene, Carbon nanotubes and even molecule, opening new experimental opportunities in quantum physics.
2
To circumvent impedance mismatch limitation, different types of on-chip photon detectors have been developed using a second nearby quantum conductor and exploiting its photon detection ability. On-chip detectors have been realized using GaAs/AlGaAs 2D electron gas patterned quantum dots [9, 10] and Aluminium or Niobium SIS junctions [11, 12, 13, 7]. The photonresponse of quantum dots depends on an energy scale set by their geometry, that of superconducting junctions is limited by a characteristic energy gap and both systems show tunnel resistance variability. Regarding bolometric detectors their efficiency depends on the phonon relaxation time, requires low temperature and shows slow response time.
In this letter, we propose a novel on-chip radiation detection based on PASN. When a quantum conductor is submitted to a time dependent drainsource voltage, electrons and holes are created which then scatter inside the conductor. Their partitioning between source and drain contacts leads to a current noise called Photo-Assisted Shot Noise. Remarkably, there is a simple link between PASN and the incident radiation power up to a noise Fano factor characterizing the statistics of partitioning. This simple link is better understood if we remark that PASN is the quantum manifestation of the rectification property of ordinary shot noise [18, 19, 20, 21] which is proportional to the absolute value of the drain-source voltage.
Figure 1 shows the principle of the on-chip detection. It consists of two separate excitation and measurement circuit lines etched in a high mobility two-dimensional electron gas (2DEG). Each line involves two QPCs in se-
3
ries. On the upper line, the left QPC is the high-frequency emitter. When
biased by the dc voltage VdEs it generates shot noise up to the frequency eVdEs /h [20, 22]. The right QPC tuned on a conductance plateau acts as a stable series resistance RSE converting current noise into voltage noise. In
the lower line the left QPC is the detector. In series with the right QPC,
also tuned on a resistance plateau RSD, it experiences the emitter line volt-
age fluctuations via the coupling capacitance CC up to the cut-off frequency
fmax [23]. The number of electron-hole pairs generated in the detector line
is a direct function of the radiated noise power integrated up to frequency
m
i
n
(
e
V
E ds
/
h
,
f
m
a
x
)
.
Their scattering by the QPC detector generates a low-
frequency PASN which is measured. fmax depends on all QPC resistances
and on the self-capacitance Cself of the 2DEG part between the QPCs in
series.
To understand the photon detection principle, let us first assume that the
detector line is excited by a coherent radiation at frequency Ω/2π such that
VdEs (t) = Vac cos(Ωt). Electrons in the detector line can absorb l photons of
energy El=l Ω by creating an electron-hole pair with a probability P (El)=
| Jl(eVac/ Ω) |2, with Jl the lth Bessel function. Electrons and holes are
independently and randomly partitioned by the QPC detector between left
and right contacts. This generates a PASN whose low-frequency spectral
density of current fluctuations SIP ASN is given by [14, 15, 16, 17]:
4
SP ASN
2e2 = [4kBTe
D2 +
I
h
D,n
n
l=+∞
El
2 DD,n(1 − DD,n)
ElP (El) coth 2kBTe ]
(1)
n
l=−∞
with Te the electronic temperature and DD,n the transmission of the nth electronic mode through the detector QPC, n=1, 2, ... . For weak ac voltage eVac ≪ Ω and zero temperature a direct relation can be established between the radiation power Prad = Va2c/2Zrad and the current noise: SIP ASN ≃ 2GDF (Zrade2/ )Prad/Ω, where Zrad is the radiation impedance assumed smaller than the QPC detector conductance GD and F the Fano factor.
From Eq. (1), it is clear that the maximum PASN will be obtained for total transmission DD = n DD,n = k + 1/2, k an integer. In addition to shot noise, a photon assisted dc current Iph is generated when considering the (weak) energy dependence of the QPC transmission :
I = 2e dǫ(− ∂f )( ∂DD,n ) l=+∞ E2P (E )
(2)
ph h
∂ǫ
∂ǫ
l
l
n
l=−∞
f (ǫ) is the equilibrium Fermi distribution. Modeling the QPC transmission with a saddle point potential [24, 25], it can be shown that ∂D∂Dǫ ,n ∝ DD,n(1−DD,n): maximum photocurrents will be also obtained at half-integer
DD.
5
In the present case, the excitation is not coherent but due to random fluctuations of the QPC detector drain-source voltage which originates from the capacitive coupling with the noisy QPC emitter. The above expressions can be generalized, giving the PASN as:
SP ASN
2e2 = [4kBTe
D2 +
I
h
D,n
n
E
2 DD,n(1 − DD,n) EP (E) coth 2kBTe dE]
(3)
n
and the photocurrent:
Iph = 2e dǫ(− ∂f )( ∂DD,n ) E2P (E)dE
(4)
h ∂ǫ n ∂ǫ
The generalized probability distribution P (E) is similar to the P (E) function
used in the dynamical Coulomb blockade theory (see Supplementary Infor-
mation). It is a direct function of the radiation power to be detected, which
as a shot noise itself is maximum for DE = 0.5.
We first focus on the photocurrent whose measurement set-up is described
in Fig. 2(a). Source Vin leads to a current in the upper line and to the
voltage difference VdEs across the emitter. The resulting shot noise induces
a photocurrent Iph in the detector. We modulate Vin at frequency 174 Hz
and detect the induced photocurrent using lock-in techniques. Series resis-
tances are tuned on a plateau for each line while the emitter and detector
6
transmissions are varied. Following the saddle point potential model of a QPC [24, 25], the transmission of the nth mode can be written DD,n(Vg) = 1/(1+e2π(V0−Vg)/Vg,n) where Vg,n is related to the negative curvature of the saddle point potential. The photocurrent is given by (see Supplementary Information):
Iph = e 1 kBTE∗ e2
2π DD,n(1 − DD,n)
(5)
h ∆ Cself n Vg,n
Vg,n and the lever arm ∆ = ∂ǫ/∂Vg are extracted from a study of the differential QPC conductance versus gate and bias voltages. We have introduced TE∗ as the effective noise temperature of the circuit which, up to a coupling factor, includes a combination of the shot noise temperature of the emitter: (1 − DE) e2VkdBEs plus other equilibrium thermal noise contributions of the circuit surrounding the detector QPC (see the supplementary Information).
The color plot in Fig. 2(b) shows the measured photocurrent as a function of the emitter and detector transmissions DE and DD, up to two transmitting orbital electronic modes. Above the color plot, the photocurrent is plotted as a function of DD for a fixed value of DE ∼ 0.45. As expected, it is maximum for half transmission of the emitter electronic modes and vanishes for integer transmission. These measurements have been found essential for a fine calibration of the electrical circuit and for complementary characterization of the photon-assisted shot noise effect (see the Supplementary Information).
7
We now consider PASN measurements. The cross correlation noise measurement set up is described in Fig. 3(a). To characterize the detector line, the QPC detector transmission is set to DD = 0.5 while a dc bias is applied on the detector line. The resulting shot noise measured, black dots in Fig. 3(b), perfectly agrees with the theory in red solid line. We extract an electronic temperature Te = 310 mK close to the fridge temperature T = 300 mK . Then we turn off the applied bias on the detector line and the QPC emitter is biased and also tuned at transmission DE = 0.5. Both series resistances are tuned on the first plateau. Because of the coupling capacitance, voltage fluctuations are reported on the detector line. The only dc current flowing through the detector line being the weak dc photocurrent, no detectable transport shot noise is expected. However, we detect some noise, confirming that the PASN detection works as illustrated in Fig. 3(c), black circle. The detected PASN, ∆SIP ASN,D, is expected to be:
∆SP ASN,D
≃
4e2 − DD(1
−
DD)
e2
TE∗
(6)
I
h
Cself 6Te
Here, considering P (E) takes only important values for E ≪ kBTe, a lowenergy expansion of Eq. (3) has been made. The TE∗ (VdEs )/Cself amplitude compatible with the detector geometry (estimated Cself =3 fF and Cc=1 fF) and obtained from photocurrent measurements can now be compared to the noise measurement. The theoretical prediction (red solid line) following Eq. 6 also includes an additional term due to heating effect. We discuss this
8
point in the following.
We open the series QPC of the detector line such that the current to voltage fluctuation conversion is now mediated by the smaller resistance of the long resistive mesa. Then we apply a fixed bias VdDs and sweep the detector transmission (red circles in Fig. 4(a)). As expected the shot noise is maximum for DD = 0.5 and cancels for DD = 1. The slight disagreement with the theoretical prediction (red solid line) around DD ∼ 0.7 reveals a weak ”0.7” anomaly [26, 27, 28, 29]. Then we tune the series QPC on its first plateau and repeat the same experiment (black circles). Surprisingly, the shot noise does not cancel anymore for DD = 1. To understand it, we must consider heating effects. Since the size of the QPC is much smaller than the electron-phonon relaxation length, there is a temperature gradient from the QPC to the ohmic contacts assumed to be at the base temperature of the fridge. Combining Joule heating together with the Wiedemann-Franz law, we obtain [18]:
Te(Vds) = T 2 + 24 G (1 + 2G )( eVds )2
(7)
fridge π2 Gm
Gm 2kB
with Gm the total conductance linking the QPC to the ohmic contacts, and Tfridge the base temperature. Considering this effect, a QPC tuned on a plateau will not be noiseless anymore. We find a good agreement with measurements, black solid line.
9