Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0211618

Electrical quantum measurement of a two-level system at arbitrary voltage and temperature

Alexander Shnirman, Dmitry Mozyrsky, Ivar Martin

Published Nov 27, 2002• 1 citation
arXivHTMLPDF

Abstract

We calculate the noise spectrum of the output signal of a quantum detector during continuous measurement of a two-level system (qubit). We generalize the previous results obtained for the regime of high voltages (when $eV$ is much larger than the qubit's energy level splitting $Δ$) to the case of arbitrary voltages and temperatures. When $V \sim Δ$ the output spectrum is essentially asymmetric in frequency, i.e., the output signal is no longer classical. In the emission (negative frequency) part of the spectrum the peak due to the qubit's coherent oscillations can be 8 times higher that the background pedestal. For $V < Δ$ and T=0 the coherent peaks do not appear at all.

DOI
10.48550/arxiv.cond-mat/0211618

Related papers

Output spectrum of a measuring device at arbitrary voltage and temperature

Alexander Shnirman, Dmitry Mozyrsky, Ivar Martin

We calculate the noise spectrum of the electrical current in a quantum point contact which is used for continuous measurements of a two-level system (qubit). We generalize the previous results obtained for the regime of high transport voltages (when V is much larger than the qubit's energy level splitting B (we put e = ℏ = 1)) to the case of arbitrary voltages and temperatures. When V ∼ B , the background output spectrum is essentially asymmetric in frequency, i.e. , it is no longer classical. Yet, the spectrum of the amplified signal, i.e. , the two coherent peaks at ω = ± B , is still symmetric. In the emission (negative frequency) part of the spectrum the coherent peak can be 8 times higher than the background pedestal. Alternatively, this ratio can be seen in the directly measureable excess noise. For V < B and T = 0 the coherent peaks do not appear at all. We relate these results to the properties of linear amplifiers.

arXiv:cond-mat/0311325•Europhysics Letters (EPL)•Aug 25, 2004•25 citations

Output spectrum of a detector measuring quantum oscillations

Alexander N. Korotkov

We consider a two-level quantum system (qubit) which is continuously measured by a detector, and calculate the spectral density of the detector output. In the weakly coupled case the spectrum exhibits a moderate peak at the frequency of quantum (Rabi) oscillations and a Lorentzian-shape increase of the detector noise at low frequency. As the coupling increases, the spectrum transforms into a single Lorentzian corresponding to random jumps between two states. We prove that the Bayesian formalism for the selective evolution of the density matrix gives the same spectrum as the conventional master equation approach, despite the significant difference in interpretation. The effects of the detector nonideality and the finite-temperature environment are also discussed.

arXiv:cond-mat/0003225•Physical review. B, Condensed matter•Feb 5, 2001•97 citations

Noise and measurement backaction in superconducting circuits: qubits as spectrometers of quantum noise

Robert J. Schoelkopf, Aashish A. Clerk, S. M. Girvin +2 more

Electrical engineers and physicists are naturally very interested in noise in circuits, amplifiers and detectors. With the advent of quantum computation and other high frequency electronics operating at low temperatures, we have entered a regime where quantum noise and quantum-limited detectors are important. Here we describe the general concept of a two-level system as a quantum spectrum analyzer and apply it to a simple superconducting qubit, the Cooper-pair box. We then discuss the coupling of a Cooper-pair box to its electromagnetic environment, whose noise leads to a finite polarization and excited-state lifetime of the qubit. Finally, we describe a theoretical technique for treating a qubit coupled to a measurement system, which allows one to calculate the full quantum noise of the measurement device. We present results for such a calculation for the case of a normal SET.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 9, 2003•7 citations

Detection of Quantum Noise from an Electrically Driven Two-Level System

R. Deblock, Eugen Onac, Leonid Gurevich +1 more

The electrical noise of mesoscopic devices can be strongly influenced by the quantum motion of electrons. To probe this effect, we have measured the current fluctuations at high frequency (5 to 90 gigahertz) using a superconductor-insulator-superconductor tunnel junction as an on-chip spectrum analyzer. By coupling this frequency-resolved noise detector to a quantum device, we can measure the high-frequency, nonsymmetrized noise as demonstrated for a Josephson junction. The same scheme is used to detect the current fluctuations arising from coherent charge oscillations in a two-level system, a superconducting charge qubit. A narrow band peak is observed in the spectral noise density at the frequency of the coherent charge oscillations.

arXiv:cond-mat/0310180•Science•Jul 10, 2003•176 citations

Spectrum of qubit oscillations from generalized Bloch equations

Rusko Ruskov, Alexander N. Korotkov

We have developed a formalism suitable for calculation of the output spectrum of a detector continuously measuring quantum coherent oscillations in a solid-state qubit, starting from microscopic generalized Bloch equations. The results coincide with those obtained using Bayesian and master equation approaches. The previous results are generalized to the cases of arbitrary detector response and finite detector temperature.

arXiv:cond-mat/0202303•Physical review. B, Condensed matter•Feb 5, 2003•37 citations

Measurement of a qubit and measurement with a qubit

Antonio Di Lorenzo

Generally, the measurement process consists in coupling a system to a detector that can give a continuous output. However, it may be interesting to use as a detector a system with a discrete spectrum, especially in view of applications to quantum information. Here, we study 1) a two-level system measuring another two-level system (qubit); 2) a generic system measuring a qubit; 3) a qubit measuring a generic system. The results include the case when a postselection on the measured system is made. We provide the exact solution, and also a controlled expansion in the coupling parameter, giving formulas valid in the weak measurement regime for arbitrary preparation and postselection. The concept of generalized Wigner functions is introduced.

arXiv:1302.0882•Feb 4, 2013•1 citation
We calculate the noise spectrum of the output signal of a quantum detector during continuous measurement of a two-level system (qubit). We generalize the previous results obtained for the regime of high voltages (when eVeVeV is much larger than the qubit's energy level splitting ΔΔΔ) to the case of arbitrary voltages and temperatures. When V∼ΔV \sim ΔV∼Δ the output spectrum is essentially asymmetric in frequency, i.e., the output signal is no longer classical. In the emission (negative frequency) part of the spectrum the peak due to the qubit's coherent oscillations can be 8 times higher that the background pedestal. For V<ΔV < ΔV<Δ and T=0 the coherent peaks do not appear at all.
We calculate the noise spectrum of the electrical current in a quantum point contact which is used for continuous measurements of a two-level system (qubit). We generalize the previous results obtained for the regime of high transport voltages (when V is much larger than the qubit's energy level splitting B (we put e = ℏ = 1)) to the case of arbitrary voltages and temperatures. When V ∼ B , the background output spectrum is essentially asymmetric in frequency, i.e. , it is no longer classical. Yet, the spectrum of the amplified signal, i.e. , the two coherent peaks at ω = ± B , is still symmetric. In the emission (negative frequency) part of the spectrum the coherent peak can be 8 times higher than the background pedestal. Alternatively, this ratio can be seen in the directly measureable excess noise. For V < B and T = 0 the coherent peaks do not appear at all. We relate these results to the properties of linear amplifiers.
We consider a two-level quantum system (qubit) which is continuously measured by a detector, and calculate the spectral density of the detector output. In the weakly coupled case the spectrum exhibits a moderate peak at the frequency of quantum (Rabi) oscillations and a Lorentzian-shape increase of the detector noise at low frequency. As the coupling increases, the spectrum transforms into a single Lorentzian corresponding to random jumps between two states. We prove that the Bayesian formalism for the selective evolution of the density matrix gives the same spectrum as the conventional master equation approach, despite the significant difference in interpretation. The effects of the detector nonideality and the finite-temperature environment are also discussed.
Electrical engineers and physicists are naturally very interested in noise in circuits, amplifiers and detectors. With the advent of quantum computation and other high frequency electronics operating at low temperatures, we have entered a regime where quantum noise and quantum-limited detectors are important. Here we describe the general concept of a two-level system as a quantum spectrum analyzer and apply it to a simple superconducting qubit, the Cooper-pair box. We then discuss the coupling of a Cooper-pair box to its electromagnetic environment, whose noise leads to a finite polarization and excited-state lifetime of the qubit. Finally, we describe a theoretical technique for treating a qubit coupled to a measurement system, which allows one to calculate the full quantum noise of the measurement device. We present results for such a calculation for the case of a normal SET.
The electrical noise of mesoscopic devices can be strongly influenced by the quantum motion of electrons. To probe this effect, we have measured the current fluctuations at high frequency (5 to 90 gigahertz) using a superconductor-insulator-superconductor tunnel junction as an on-chip spectrum analyzer. By coupling this frequency-resolved noise detector to a quantum device, we can measure the high-frequency, nonsymmetrized noise as demonstrated for a Josephson junction. The same scheme is used to detect the current fluctuations arising from coherent charge oscillations in a two-level system, a superconducting charge qubit. A narrow band peak is observed in the spectral noise density at the frequency of the coherent charge oscillations.
Generally, the measurement process consists in coupling a system to a detector that can give a continuous output. However, it may be interesting to use as a detector a system with a discrete spectrum, especially in view of applications to quantum information. Here, we study 1) a two-level system measuring another two-level system (qubit); 2) a generic system measuring a qubit; 3) a qubit measuring a generic system. The results include the case when a postselection on the measured system is made. We provide the exact solution, and also a controlled expansion in the coupling parameter, giving formulas valid in the weak measurement regime for arbitrary preparation and postselection. The concept of generalized Wigner functions is introduced.