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Journal of the Optical Society of America B

Squeezed-state generation using a Josephson parametric amplifier

Bernard Yurke

Published Oct 1, 1987• 83 citations
Publisher

Abstract

Josephson-junction parametric amplifiers are promising candidates as sources of squeezed microwave radiation. Here, an analysis of one such amplifier, a radio-frequency superconducting quantum interference device operated in either the three-photon or the four-photon mode, is presented. Expressions for the amount of squeezing that could be obtained from such a device are derived in terms of the basic device parameters.

DOI
10.1364/josab.4.001551

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Josephson-junction parametric amplifiers are promising candidates as sources of squeezed microwave radiation. Here, an analysis of one such amplifier, a radio-frequency superconducting quantum interference device operated in either the three-photon or the four-photon mode, is presented. Expressions for the amount of squeezing that could be obtained from such a device are derived in terms of the basic device parameters.
The successful generation and detection of squeezed electromagnetic radiation at optical frequencies1 promise to open the door to the exploration of new quantum phenomena, some of which may be technologically useful.2 The generation and detection of squeezed radiation at low frequencies would also open the door to the observation of novel quantum phenomena. We report here on a Josephson parametric amplifier which appears to be well behaved and may be suitable for generating squeezed coherent microwave radiation. The amplifier was operated in the four-photon or doubly degenerate mode,3 and thus its operation is akin to that of an optical four-wave mixer.1
We present the results of an experimental effort to generate squeezed microwave radiation using the phase-sensitive gain of a Josephson parametric amplifier. To facilitate the interpretation of the experimental results, we first present a discussion of the theory of microwave squeezing via Josephson parametric amplifiers. This is followed by a detailed description of the device fabricated for our experiment. Experimental results are then presented for the device used in both the doubly degenerate or four-photon mode and for the degenerate or three-photon mode. We have observed parametric deamplification of signals by more than 8 dB. We have demonstrated squeezing of 4.2-K thermal noise. When operated at 0.1 K, the amplifier exhibits an excess noise of 0.28 K when referred to the input. This is smaller than the vacuum fluctuation noise level \ensuremath{\Elzxh}\ensuremath{\omega}/2k=0.47 K. The amplifier is thus quieter than a linear phase-insensitive amplifier in principle can be.
Three-wave mixing devices, i.e. non-linear circuits converting power among three microwave signals, are key elements of analog information processing in the microwave domain. However, they are based on dissipative components such as semiconductor diodes, or SIS tunnel junctions biased near the superconducting gap. The loss of signal limits their operation and also introduces noise above the minimum required by quantum mechanics. By using Josephson junctions and superconducting resonators, we've been able to build such a quantum device. In its amplification mode, this device can be used as a preamplifier in many experiments where a few photon wide microwave signals must be measured by commercial instruments, which are sensitive to powers several orders of magnitude larger. The price to pay for this amplification is the necessary degradation of information. Indeed, an extension of the no-cloning theorem imposes that a linear phase preserving amplifier adds at least half a quantum of noise to the signal. By amplifying the finite frequency noise emitted by an NIN tunnel junction, we demonstrated that the total measurement chain adds less than 2.3 quanta to this limit thanks to our device. The operating principle of this device is based on Josephson parametric amplification. I will explain this mechanism and present results which illustrate that it can generate quantum correlated pairs of spatially separated photons with different wavelengths known as two-mode squeezed states. This experiment exploits the tunability of our device and the ease-of-use inherent to micro-wave circuits to perform a quantum optics experiment demonstrating this entanglement.
The master equation for a dc-pumped degenerate Josephson parametric amplifier is derived. It is shown that the Wigner distribution representation of this master equation can be approximated by a Fokker-Planck equation. By using this equation, the dynamical behavior of this degenerate Josephson amplifier with respect to squeezing of the radiation field is investigated. It is shown that below threshold of parametric oscillation, a squeezed vacuum state can be generated, and above threshold a second bifurcation point exists, where the device generates amplitude squeezed radiation. Basic relations between the achievable amplitude squeezing, the output power, and the operation frequency are derived.
We are engaged in an experimental effort to generate and detect squeezed vacuum fluctuations at microwave frequencies using a Josephson parametric amplifier. We have demonstrated 42% deamplification of 4.2-K thermal noise at 19.4 GHz. At this frequency the vacuum fluctuation noise is an order of magnitude smaller than 4.2-K thermal noise. We have installed cryogenic HEMT amplifiers in our apparatus, thereby increasing the detector sensitivity by an order of magnitude. Josephson parametric amplifiers have been notorious for exhibiting excess noise whose origin is still controversial. We have performed a systematic study of the noise performance of our device both below and above threshold in a variety of modes of operation. The experiments indicate that the excess noise in our device arises from low-frequency noise (0-20 MHz) propagating down dc bias lines. When an intense coherent oscillation is present in the signal passband, such as the pump when the amplifier is in the four-photon mode or the period doubled oscillations when the amplifier is operated in the three-photon mode above threshold, the low- frequency noise mixes with the coherent oscillation to generate noise sidebands in the amplifier's passband. Nevertheless, in suitable conditions, extremely low noise and high gains were achieved.
Three-wave mixing devices, i.e. non-linear circuits converting power among three microwave signals, are key elements of analog information processing in the microwave domain. However, they are based on dissipative components such as semiconductor diodes, or SIS tunnel junctions biased near the superconducting gap. The loss of signal limits their operation and also introduces noise above the minimum required by quantum mechanics. By using Josephson junctions and superconducting resonators, we've been able to build such a quantum device. In its amplification mode, this device can be used as a preamplifier in many experiments where a few photon wide microwave signals must be measured by commercial instruments, which are sensitive to powers several orders of magnitude larger. The price to pay for this amplification is the necessary degradation of information. Indeed, an extension of the no-cloning theorem imposes that a linear phase preserving amplifier adds at least half a quantum of noise to the signal. By amplifying the finite frequency noise emitted by an NIN tunnel junction, we demonstrated that the total measurement chain adds less than 2.3 quanta to this limit thanks to our device. The operating principle of this device is based on Josephson parametric amplification. I will explain this mechanism and show preliminary results which illustrate that it can generate quantum correlated pairs of spatially separated photons with different wavelengths known as two-mode squeezed states. This experiment exploits the tunability of our device and the ease-of-use inherent to micro-wave circuits to perform a quantum optics experiment demonstrating this entanglement.