1376 zyxwvutsrqponm I IEEE TRANSACTIONS ON MAGNETICS, VOL. zyxwv 25, NO. 2, MARCH 1989 BEATING THE QUANTUM LIMIT IN SIS MIXERS Michael J. Wengler and Mark F. Bocko Department of Electrical Engineering University of Rochester Rochester, zyxwvut NY 14627 Abstract A phase-sensitive amplifier is not subject to the same quantum noise restrictions as a phase-insensitive amplifier such as a normal SIS mixer. Elsewhere in this journal, Bocko, Wengler, and Zhang [ l ] present an SIS mixer which is made phase-sensitive through the use of two Lo’s. In this paper, the 2LO mixer is analyzed in the low-LO-power limit for a perfect SIS diode. The result is that a 2LO SIS mixer can beat the noise performance of a one-LO mixer by a factor of two. We are confident that even lower noise is possible with an SIS when operated in some other way. Squeezed States The quantum theory of radiation predicts the existence of pho- ton states which have different noise levels in their two quadrature phases. Squeezed states have been generated and measured at optical frequencies [2,3]. Thermal noise has been squeezed and measured at 22 GHz, but the quantum limit has not yet been exceeded. In this paper, we consider a new mixing mode involving two Lo’s. Experiments with this 2LO mixer will be carried out at 65 GHz. The squeezed state we are interested in can best be described by using voltage operators for waves traveling on a transmission line. Consider, for instance, the signal frequency radiation traveling towards a detector element. Let zyxwvutsrqp v, represent the operator for the voltage phasor in this mode. This voltage phasor is proportional to the photon operator zyxwvutsrqpon ai, for more about this see [5]. The voltage operator is not Hermitian, but it can be written in terms of Hermitian operators for the zyxwvutsrq 4, = 0 and zyxwvutsrqp 7r/2 phases of the signal, vs = ‘u,o + Z ’ u , : . zyxwvutsrqpon (1) The two Hermitian operators for the quadrature voltages which make up the voltage phasor are like the position and momentum operators in quantum mechanics, they do not commute. It is not possible to create a radiation state which yields perfectly predictable voltages for both quadratures simultaneously. This is the reason for a quantum lower limit to measurement noise. However, it is possible to create a radiation state which is an eigenstate of one of the signal quadratures. If a device can be built which measures only this quadrature of the signal, it may well measure it noiselessly, as shown by Caves [6]. Such a state is called a “squeezed” state because the noise is squeezed out of one phase while noise in the other quadrature is increased. Bocko, Wengler, and Zhang [l] propose a system for measur- ing a squeezed state in another paper in this issue, which will be referred to here as BWZ. This system is a superconducting tunnel diode (SIS) heterodyne system with a variation. Two local oscilla- tors simultaneously pump the SIS. They are at angular frequencies Manuscript rcceivcd August 22, 1988 - 1 - - zyxw w, fw, where w, is the input signal frequency and w, is the mixer output frequency. BWZ also develops a theoretical framework for analyzing the 2LO SIS mixer. In this paper, we present an analytic calculation of 2LO SIS mixer performance. This calculation simplifies the formalism of BWZ assuming 1) a “perfect” SIS, 2) low output frequency (U, << U,), and low LO power levels. This same set of assumptions leads to quantum limited performance in the one-LO SIS mixer [5]. Regular Heterodyne Detection with an SIS Wengler and Woody [SI describe a quantum theory of mixing which they apply to a superconducting tunnel diode (SIS) mixer pumped with a single LO. They calculate the noise for an idealized mixer, namely one based on an SIS with a “perfect” current-voltage curve, operated at a fairly low output frequency, pumped with a low LO power. In units of “photons referred to the input”, this mixer has added noise 1 1 A=---. ’72 (2 1 zyxwvut 17 is the matching factor between the signal source admittance, Ys, and the admittance presented by the SIS to large signals at the signal frequency, Y,, G, and G, are the real parts of zyxw 1; and Ii, respectively. Caves shows that quantum mechanics requires A 2 1/2 for a regular mixer [6]. The SIS mixer is capable of achieving quantum limited noise when the signal is properly matched to it so that 17 = 1 in (3). Wengler and Woody actually calculate the total measurement noise of a one-LO mixer used to measure a Glauber coherent state, A‘=*4+-=-. 1 1 2 ‘ 7 The extra half photon of noise comes from noise in the signal radiation state. For a Glauber coherent state, Psbs~ = 1/2, see (27) below. If a photoconductor or photon-counter of any sort is used as the mixing element for optical heterodyning, its noise is also described by (4), see, for instance, Kingston [7]. For the optical heterodyning case, 11 is the fraction of light incident on the photodetector which is absorbed into the photoconductor, in very close analogy to its meaning for the SIS mixer. For the optical heterodyne case, N can be interpreted as being entirely due to photon-counting noise in the photodetector. The similarity of the SIS result to the optical case suggest that this is the case for the SIS as well: noise in an ideal SIS mixer is simply due to photon counting statistics. 0018-9464/89/0300-1376$01 .WO 1989 IEEE