Nonequilibrium spin noise and noise of susceptibility

Abstract

We analyze out-of-equilibrium fluctuations in a driven spin system and relate them to the noise of spin susceptibility. In the spirit of the linear response theory we further relate the noise of susceptibility to a 4-spin correlation function in equilibrium. We show that, in contrast to the second noise (noise of noise), the noise of susceptibility is a direct measure of non-Gaussian fluctuations in the system. We develop a general framework for calculating the noise of susceptibility using the Majorana representation of spin-1/2 operators. We illustrate our approach by a simple example of non-interacting spins coupled to a dissipative (Ohmic) bath.PACS numbers: 85.25. Dq, 85.25.Am Noise in electronic circuits provides information about the microscopic structure of the system complementary to that obtained from linear response transport measurements 1,2 . For electronic circuits, the standard JohnsonNyquist noise is intimately related to dissipative processes with typical time scales of the order of picoseconds. At low frequencies it is "white", i.e. frequencyindependent. In contrast, the ubiquitous 1/f noise is related to slow processes, e.g., to slow rearrangements of impurities or the internal dynamics of two-level systems 3 . Its power spectrum is commonly described by the Hooge's law 4,5 , S V (f ) ∝ V 2 /f , where V is the average observed voltage. This suggests that this noise could only be observed out of equilibrium. But this was shown not to be the case by Voss and Clarke 6,7 , who measured the low-frequency fluctuations of the mean-square Johnson voltage in equilibrium (i.e., the second noise or noise of noise) and showed that these fluctuations possess a 1/f -like spectrum.Motivated by these experiments, Beck and Spruit 8 calculated the variance of the Johnson-Nyquist noise and showed that it comprised two contributions. The first one could be interpreted as arising from resistance fluctuations with a 1/f spectrum. The second, with a white spectrum, is intrinsic to any Gaussian fluctuating quantity. Consequently the equilibrium 1/f noise could only be observed at very low frequencies.From a technical point of view the variance of noise is described by a four-point correlation function 1,8 . Such objects appear also in other physical contexts. For example, Weissman 9,10 has proposed to distinguish the droplet and hierarchical models of spin glasses by the properties of the second noise, which can be expressed in terms of a particular four-spin correlation function.More recently, the problem of 1/f noise has attracted much attention in the field of superconducting quantum devices. Flux noise measurements initially performed with relatively large SQUIDs showed the 1/f behavior 11 .In the last decade similar effect has been observed in nanoscale quantum circuits 12-23 . Remarkably, the noise magnitude appears to be "universal", i.e., of the same order of magnitude for a wide range of device sizes. This noise is believed to originate from an assemblage of spins localized at the surface or interface lay...

Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits

“…Our model provides a qualitative description of the origin of fluctuations in the electrical susceptibility of mesoscopic circuits, an area which has recently started to attract attention from both experiment and theory [21][22][23] . We also note that interactions between TLS have recently been observed directly in two strongly coupled defects 24 and that such coupling has been invoked as a model of noise before, e.g.…”

Majorana representation for dissipative spin systems

“…(42). For completeness, we show the result, which is put into context and interpreted in detail elsewhere [25].…”

“…In lower orders Majorana propagators are never connected by a bosonic line. Such an element only appears in higher orders or in higher correlation functions as discussed in [25]. An example is shown in Fig.…”

“…while the noise spectrum [30] is determined by a different 2-point correlator, T K S cl α (t)S cl α (t ) . Below in Section 2, we will be interested in a specific 4-point function that determines the experimentally accessible noise of susceptibility [25,26]…”

“…We illustrate our general arguments by a specific example. For a model of paramagnetic spins coupled to an Ohmic bath [24] we determine the four-point correlation function describing the noise of susceptibility [25]. This quantity is closely related to the recently measured inductance fluctuations in SQUIDs [26].…”