Passage-time distributions from a spin-boson detector model

We investigate heat transport between two thermal reservoirs that are coupled via a large spin composed of N identical two level systems. One coupling implements the dissipative Dicke superradiance. The other coupling is locally of the pure-dephasing type and requires to go beyond the standard weak-coupling limit by employing a Bogoliubov mapping in the corresponding reservoir. After the mapping, the large spin is coupled to a collective mode with the original pure-dephasing interaction, but the collective mode is dissipatively coupled to the residual oscillators. Treating the large spin and the collective mode as the system, a standard master equation approach is now able to capture the energy transfer between the two reservoirs. Assuming fast relaxation of the collective mode, we derive a coarse-grained rate equation for the large spin only and discuss how the original Dicke superradiance is affected by the presence of the additional reservoir. Our main finding is a cooperatively enhanced rectification effect due to the interplay of supertransmittant heat currents (scaling quadratically with N ) and the asymmetric coupling to both reservoirs. For large N , the system can thus significantly amplify current asymmetries under bias reversal, functioning as a heat diode. We also briefly discuss the case when the couplings of the collective spin are locally dissipative, showing that the heat-diode effect is still present. I. MOTIVATIONThe study of radiative effects in two-level systems has a long history. Here, the spin-boson model [1] takes a very prominent role. Originating from the interaction of a two-level atom with the electromagnetic field [2], it is often used as a toy model in many other contexts. Not surprisingly, it has become a canonical model to explore fundamental methods of open systems [3][4][5] and effectively arises in a rather large number of physical systems and effects, including e.g. the dynamics of light-harvesting complexes [6], detectors [7], and the interaction of quantum dots with generalized environments [8].Ideally, one aims at a reduced description taking only the finite-dimensional spin dynamics into account. However, when the number of spins is increased, the curse of dimensionality -the exponential growth of the system Hilbert space with its size -usually inhibits investigations of large spin-boson models. When additional symmetries come into play -e.g. when the spins have the same splitting and couple collectively to all other componentssimplified descriptions are applicable. Collective effects may for example dramatically influence the dephasing behavior of the environment, leading to phenomena such as super-and sub-decoherence [9,10]. Furthermore, they play a significant role in the modelling of light-harvesting complexes [11][12][13][14]. Perhaps one of the clearest manifesta- * gernot.schaller@tu-berlin.de tions of collective behaviour is Dicke superradiance [15]. Here, the collectivity of the coupling between N two-level atoms and a low-temperature bosonic reservoir induces an...

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“…Inserting the transformation (7) and comparing with the desired form above, we find that it gives rise to two further constraints…”

Section: B Explicit Bogoliubov Mappingmentioning

confidence: 99%

Collective couplings: Rectification and supertransmittance

2016

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“…The theoretical treatment of time observables is one of the important loose ends of quantum theory. Among them the time of arrival (TOA) has received much attention lately [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16], for earlier reviews see [17,18]. A major challenge is to find the connection between ideal TOA distributions, defined for the particle in isolation, formally independent of the measurement method, and operational ones, explicitly dependent on specific measurement models and procedures.…”

Section: Introductionmentioning

confidence: 99%

Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival

2008

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Repeated measurements of a quantum particle to check its presence in a region of space was proposed long ago (G. R. Allcock, Ann. Phys. 53, 286 (1969)) as a natural way to determine the distribution of times of arrival at the orthogonal subspace, but the method was discarded because of the quantum Zeno effect: in the limit of very frequent measurements the wave function is reflected and remains in the original subspace. We show that by normalizing the small bits of arriving (removed) norm, an ideal time distribution emerges in correspondence with a classical local-kineticenergy distribution.

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“…The present detector model is applicable not only to arrival-time measurements, but also to more involved tasks like a measurement of passage times. A detailed analysis including numerical examples will appear elsewhere [32]. It turns out that a too weak spin-bath coupling yields a broad passage-time distribution due to the slow response of the detector to the presence of the particle.…”

Section: Discussion and Extensionsmentioning

confidence: 99%

“…There is, however, an intermediate range for A(x) yielding rather narrow passage-time distributions. Indeed, a rough estimate in [32] shows that for an optimal choice of incident wave packet and decay rate A(x) the precision of the measurement can be expected to behave like E −3/4 , where E is the energy of the incident particle. For low velocities, this means some improvement as compared to the results of models coupling the particle continuously or semi-continuously to a clock, where one has E −1 -behavior [33,34].…”

Section: Discussion and Extensionsmentioning

confidence: 99%

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Investigation of a quantum mechanical detector model for moving, spread-out particles

Hegerfeldt¹,

Neumann²,

Schulman³

2006

J. Phys. A: Math. Gen.

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We investigate a fully quantum mechanical spin model for the detection of a moving particle. This model, developed in earlier work, is based on a collection of spins at fixed locations and in a metastable state, with the particle locally enhancing the coupling of the spins to an environment of bosons. The appearance of bosons from particular spins signals the presence of the particle at the spin location, and the first boson indicates its arrival. The original model used discrete boson modes. Here we treat the continuum limit, under the assumption of the Markov property, and calculate the arrival-time distribution for a particle to reach a specific region.

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Passage-time distributions from a spin-boson detector model

Cited by 6 publications

References 35 publications

Collective couplings: Rectification and supertransmittance

Collective couplings: Rectification and supertransmittance

Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival

Investigation of a quantum mechanical detector model for moving, spread-out particles

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