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Small-Signal Analysis of MOSFET Amplifiers

In small-signal analysis, a MOSFET transistor amplifier acts as a linear amplifier when operating in its saturation region. The gate-to-source voltage (VGS) of the MOSFET is the sum of the DC biasing voltage and the small time-varying input signal. This combination sets up the operating point and modulates the drain current (ID) that flows from the drain to the source. When a small AC signal is superimposed on the DC bias voltage at the gate, the instantaneous drain current comprises three...
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Small signal analysis is a fundamental approach used in electronics to understand how a Bipolar Junction Transistor (BJT) amplifier processes signals. In the active region, the BJT is designed for linear amplification. The transistor's behavior under these conditions is governed by its instantaneous base-emitter voltage VBE, a sum of the DC bias VBE, and a small AC signal VBE, resulting in the collector current iC. Here, the collector current has a DC component and an AC component.
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quantum time evolution in a qubit readout process with a Josephson bifurcation amplifier.

Hayato Nakano1, Shiro Saito, Kouichi Semba

  • 1NTT Basic Research Laboratories, NTT Corporation, Atsugi-shi, Kanagawa 243-0198, Japan. nakano@will.brl.ntt.co.jp

Physical Review Letters
|August 8, 2009
PubMed
Summary

Quantum mechanical analysis reveals that decoherence enables Josephson bifurcation amplifier (JBA) readout of superconducting qubits. Decoherence allows qubit-probe entanglement to separate, enabling measurement, with waiting time dependent on JBA decoherence strength.

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Area of Science:

  • Quantum computing
  • Superconducting circuits
  • Quantum measurement

Background:

  • The Josephson bifurcation amplifier (JBA) is a key component for reading out superconducting qubits.
  • Understanding the quantum mechanical dynamics of the JBA readout process is crucial for improving qubit performance.
  • Purely quantum systems do not exhibit the bifurcation phenomenon observed in JBA measurements.

Purpose of the Study:

  • To quantum mechanically analyze the Josephson bifurcation amplifier (JBA) readout process for superconducting qubits.
  • To investigate the role of decoherence in enabling JBA bifurcation and hysteresis.
  • To understand the dynamics of qubit-probe entanglement during the measurement and projection phases.

Main Methods:

  • Calculated the dynamics of the density operator for a driven nonlinear oscillator coupled to a qubit.
  • Modeled the JBA readout process by incorporating decoherence into the quantum system.
  • Analyzed the evolution of the qubit-probe entangled state during the measurement.

Main Results:

  • Decoherence is essential to reproduce the bifurcation phenomenon with finite hysteresis in the JBA readout.
  • Observed the entanglement between the qubit and the JBA, which separates into distinct states upon JBA transition (projection).
  • The waiting time for macroscopic separation of JBA states, crucial for readout, is determined by the JBA's decoherence strength.

Conclusions:

  • Decoherence is a critical factor enabling the JBA's bifurcation and facilitating superconducting qubit readout.
  • The quantum projection of the qubit state onto the JBA states is observed during the measurement process.
  • Optimizing JBA decoherence is key to controlling readout fidelity and measurement time in quantum computing.