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The horizon of Josephson point contacts
Physica B 284}288 (2000) 1854}1855
The horizon of Josephson point contacts Kurt Gloos *, Frithjof Anders Max-Planck-Institut fu( r chemische Physik fester Stowe, D-01187 Dresden, Germany Institut fu( r Festko( rperphysik, Technische Universita( t Darmstadt, Hochschulstr. 8, D-64289 Darmstadt, Germany
Abstract Josephson point contacts can have rather small dynamic capacitances of order 0.1 fF and huge plasma frequencies u *1 ps\. The quantum-mechanical zero-point #uctuations of the Josephson plasma interact with the electromag netic "eld only inside the horizon &c/u of the junction, and the dynamic capacitance turns out to be C+ic/u at a lead capacitance per length i. Those contacts can easily resist external high-frequency noise. 2000 Elsevier Science B.V. All rights reserved. PACS: 74.50.#r; 74.40.#k; 74.60.Jg; 73.40.Jm Keywords: Break junctions; Horizon model; Josephson e!ect
The supercurrent I sinu across a Josephson junction is always accompanied by a normal quasi-particle current, described by a parallel resistance R"R , as well as a displacement current due to a capacitance C, representing a short circuit for the high-frequency part of the supercurrent. Such a resistively and capacitively shunted junction can be modelled by a particle of &mass' ( /2e)C exposed to a viscous damping force ( /2eR )u in the washboard potential
E(I, u)"! Iu!E ) cos u. (# 2e
(1)
This potential contains a number of discrete energy levels, the lowest one at the zero-point energy u /2. When C is small, quantum tunneling of the phase u dominates the di!erential resistance d;(I)/dI of a weakly damped metallic Josephson junction at low temperatures, and allows to extract both Josephson coupling energy E " I/2e and plasma frequency (#
* Correspondence address. Institut fuK r FestkoK rperphysik, Technische UniversitaK t Darmstadt, Hochschulstr. 8, D-64289 Darmstadt, Germany. Tel.: #496151162784; fax: #496151164883. E-mail address: [email protected] (K. Gloos)
u "(2eI/ C from the spectra at I;I, making the capacitance an experimentally accessible parameter [1]. In contrast to planar tunnel junctions, metallic junctions or point contacts have no intrinsic static capacitance, only a dynamic one due to the distributed lead capacitance i, typically &10 pF/m. To estimate C we use a concept known in quantum mechanics: a conventional particle of mass m interacting with a #uctuating quantum electromagnetic "eld [2]. The interaction takes place in a certain volume around the particle, limited by a cut-o! parameter &c /mc to avoid additional particles being created or destroyed. For a Josephson junction"&particle in the washboard potential interacting with the electromagnetic "eld', the &creation of a particle' means to excite the system out of its ground state to the next higher level. Therefore, the internal energy mc of the conventional particle has to be replaced by the energy di!erence u between the two lowest levels, yielding &c/u as horizon. With the experimental i the dynamic capacitance C+ic/u (C)"ic /2eI becomes then a function of the critical current I [1]. We prepared metallic point contacts between two bulk pieces of the classical superconductors Pb, In, Al, and Cd, using mechanical-controllable break junctions. The differential resistance was recorded in the standard fourterminal mode with current biasing. LRC "lters at the mixing chamber protect the sample from low-frequency
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 8 7 2 - 0
K. Gloos, F. Anders / Physica B 284}288 (2000) 1854}1855
Fig. 1. (a) Power P versus plasma frequency u . For a detect able e!ect, a minimum u has to be absorbed, while not more than ppc/u can be absorbed at p"1 W/m. (b) d;(I)/dI of a Pb junction at ¹"0.1 K. Thermal radiation (heater on) reduces the zero-bias contact resistance. Switching on the LED does not further change the spectra.
(&MHz) noise. The plasma frequency as well as the coupling energy of contacts with su$ciently large residual resistance R were derived from d;(I)/dI at IP0 [1]. The analysis showed the capacitance of the junctions C+4eE / u to "t i+3.3 pF/m. (# Additional power up to about 10 lW could be applied to the junction by a light-emitting diode (LED), weakly heat-sunk at the 4 K #ange. For ignition the LED was heated to about 100 K. Its red light at u +3000 ps\ *#" was fed to the junction by a glass "bre, illuminating a &5 mm diameter spot. We applied LED power to Josephson junctions in three di!erent regimes: on lowresistance junctions with u +2000 ps\, on junctions with u +200 ps\, and on high-resistance junctions with u +10 ps\. In all three cases u *u , large *#" enough to excite transitions out of the ground state. Surprisingly, switching on the LED did not e!ect the spectra. The horizon model explains this observation (Fig. 1a). To a!ect the spectra requires the absorption of
u at a rate &u or a power & u, which increases strongly at large u . But a junction exposed to a plane wave electromagnetic "eld interacts with the "eld only
1855
inside the horizon &c/u . At an energy #ux density p, the junction can absorb not more than &pp(c/u ), decreasing strongly at large u . At an energy #ux density smaller than u (u/2pc) absorption will be further *#" reduced because there is less than one quantum inside the horizon per time interval 1/u . This corresponds to a critical frequency of u +1 ps\ at our maximum p+1 W/m. Thus, due to the small horizon, the junctions are only weakly susceptible to external high-frequency noise. Some junctions showed a zero-bias resistance maximum which we had tentatively attributed to the excitation of Bloch waves or to the Coulomb blockade of Cooper pair tunnelling, though the junctions are in the tight-binding limit [1]. Using the heater wrapped around the LED as thermal radiator with the glass "bre as transmission line, the zero-bias maxima were suppressed (Fig. 1b), with the spectra "tting well d;(I)/dI+ R cosh(3.6pI/eu ) expected for quantum tunnelling of the phase. Adding LED light did not change the spectra, as reported above. Obviously, the applied thermal radiation is too weak to excite transitions between the discrete levels of the washboard potential, that would further enhance the zero-bias resistance. But it helps to overcome the Coulomb blockade E "e/2C of about !
u /8 in our experiments. Acknowledgements This work was supported by the SFB 252 Darmstadt/Frankfurt/Mainz.
References [1] K. Gloos, F. Anders, J. Low Temp. Phys. 116 (1999) 21. [2] A. Messiah, Quantenmechanik, Vol. 2, Walter de Gruyter, Berlin, 1979, p. 429 [MeH canique Quantique, Vol. 2, Dunod, Editeur, Paris, 1964.]
The horizon of Josephson point contacts Kurt Gloos *, Frithjof Anders Max-Planck-Institut fu( r chemische Physik fester Stowe, D-01187 Dresden, Germany Institut fu( r Festko( rperphysik, Technische Universita( t Darmstadt, Hochschulstr. 8, D-64289 Darmstadt, Germany
Abstract Josephson point contacts can have rather small dynamic capacitances of order 0.1 fF and huge plasma frequencies u *1 ps\. The quantum-mechanical zero-point #uctuations of the Josephson plasma interact with the electromag netic "eld only inside the horizon &c/u of the junction, and the dynamic capacitance turns out to be C+ic/u at a lead capacitance per length i. Those contacts can easily resist external high-frequency noise. 2000 Elsevier Science B.V. All rights reserved. PACS: 74.50.#r; 74.40.#k; 74.60.Jg; 73.40.Jm Keywords: Break junctions; Horizon model; Josephson e!ect
The supercurrent I sinu across a Josephson junction is always accompanied by a normal quasi-particle current, described by a parallel resistance R"R , as well as a displacement current due to a capacitance C, representing a short circuit for the high-frequency part of the supercurrent. Such a resistively and capacitively shunted junction can be modelled by a particle of &mass' ( /2e)C exposed to a viscous damping force ( /2eR )u in the washboard potential
E(I, u)"! Iu!E ) cos u. (# 2e
(1)
This potential contains a number of discrete energy levels, the lowest one at the zero-point energy u /2. When C is small, quantum tunneling of the phase u dominates the di!erential resistance d;(I)/dI of a weakly damped metallic Josephson junction at low temperatures, and allows to extract both Josephson coupling energy E " I/2e and plasma frequency (#
* Correspondence address. Institut fuK r FestkoK rperphysik, Technische UniversitaK t Darmstadt, Hochschulstr. 8, D-64289 Darmstadt, Germany. Tel.: #496151162784; fax: #496151164883. E-mail address: [email protected] (K. Gloos)
u "(2eI/ C from the spectra at I;I, making the capacitance an experimentally accessible parameter [1]. In contrast to planar tunnel junctions, metallic junctions or point contacts have no intrinsic static capacitance, only a dynamic one due to the distributed lead capacitance i, typically &10 pF/m. To estimate C we use a concept known in quantum mechanics: a conventional particle of mass m interacting with a #uctuating quantum electromagnetic "eld [2]. The interaction takes place in a certain volume around the particle, limited by a cut-o! parameter &c /mc to avoid additional particles being created or destroyed. For a Josephson junction"&particle in the washboard potential interacting with the electromagnetic "eld', the &creation of a particle' means to excite the system out of its ground state to the next higher level. Therefore, the internal energy mc of the conventional particle has to be replaced by the energy di!erence u between the two lowest levels, yielding &c/u as horizon. With the experimental i the dynamic capacitance C+ic/u (C)"ic /2eI becomes then a function of the critical current I [1]. We prepared metallic point contacts between two bulk pieces of the classical superconductors Pb, In, Al, and Cd, using mechanical-controllable break junctions. The differential resistance was recorded in the standard fourterminal mode with current biasing. LRC "lters at the mixing chamber protect the sample from low-frequency
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 8 7 2 - 0
K. Gloos, F. Anders / Physica B 284}288 (2000) 1854}1855
Fig. 1. (a) Power P versus plasma frequency u . For a detect able e!ect, a minimum u has to be absorbed, while not more than ppc/u can be absorbed at p"1 W/m. (b) d;(I)/dI of a Pb junction at ¹"0.1 K. Thermal radiation (heater on) reduces the zero-bias contact resistance. Switching on the LED does not further change the spectra.
(&MHz) noise. The plasma frequency as well as the coupling energy of contacts with su$ciently large residual resistance R were derived from d;(I)/dI at IP0 [1]. The analysis showed the capacitance of the junctions C+4eE / u to "t i+3.3 pF/m. (# Additional power up to about 10 lW could be applied to the junction by a light-emitting diode (LED), weakly heat-sunk at the 4 K #ange. For ignition the LED was heated to about 100 K. Its red light at u +3000 ps\ *#" was fed to the junction by a glass "bre, illuminating a &5 mm diameter spot. We applied LED power to Josephson junctions in three di!erent regimes: on lowresistance junctions with u +2000 ps\, on junctions with u +200 ps\, and on high-resistance junctions with u +10 ps\. In all three cases u *u , large *#" enough to excite transitions out of the ground state. Surprisingly, switching on the LED did not e!ect the spectra. The horizon model explains this observation (Fig. 1a). To a!ect the spectra requires the absorption of
u at a rate &u or a power & u, which increases strongly at large u . But a junction exposed to a plane wave electromagnetic "eld interacts with the "eld only
1855
inside the horizon &c/u . At an energy #ux density p, the junction can absorb not more than &pp(c/u ), decreasing strongly at large u . At an energy #ux density smaller than u (u/2pc) absorption will be further *#" reduced because there is less than one quantum inside the horizon per time interval 1/u . This corresponds to a critical frequency of u +1 ps\ at our maximum p+1 W/m. Thus, due to the small horizon, the junctions are only weakly susceptible to external high-frequency noise. Some junctions showed a zero-bias resistance maximum which we had tentatively attributed to the excitation of Bloch waves or to the Coulomb blockade of Cooper pair tunnelling, though the junctions are in the tight-binding limit [1]. Using the heater wrapped around the LED as thermal radiator with the glass "bre as transmission line, the zero-bias maxima were suppressed (Fig. 1b), with the spectra "tting well d;(I)/dI+ R cosh(3.6pI/eu ) expected for quantum tunnelling of the phase. Adding LED light did not change the spectra, as reported above. Obviously, the applied thermal radiation is too weak to excite transitions between the discrete levels of the washboard potential, that would further enhance the zero-bias resistance. But it helps to overcome the Coulomb blockade E "e/2C of about !
u /8 in our experiments. Acknowledgements This work was supported by the SFB 252 Darmstadt/Frankfurt/Mainz.
References [1] K. Gloos, F. Anders, J. Low Temp. Phys. 116 (1999) 21. [2] A. Messiah, Quantenmechanik, Vol. 2, Walter de Gruyter, Berlin, 1979, p. 429 [MeH canique Quantique, Vol. 2, Dunod, Editeur, Paris, 1964.]