Deviations from exponential decay in the case of spontaneous emission from a two-level atom

We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the coherent evolution of the combined qubit-EMF system, thus allowing for the back-action from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find non-exponential decay for both the diagonal and non-diagonal matrix elements of the qubit's reduced density matrix in the pointer basis. From the diagonal elements we see the qubit relaxes to thermal equilibrium with the bath. From the non-diagonal elements, we see the decoherence rate beginning at the usually predicted thermal rate, but changing to the zero temperature decoherence rate as the qubit and bath become entangled. These two rates are comparable, as was shown before in the zero temperature case [C. Anastopoulos and B. L. Hu, Phys. Rev. A 62 (2000) 033821]. On the entanglement of a qubit with the EMF under this type of resonant coupling we calculated, for the qubit reduced density matrix, the fidelity and the von Neumann entropy, which is a measure of the purity of the density matrix. The present more accurate non-Markovian calculations predict lower loss of fidelity and purity as compared with the Markovian results. Generally speaking, with the inclusion of quantum correlations between the qubit and its environment, the non-Markovian processes tend to slow down the drive of the system to equilibrium, prolonging the decoherence and better preserving the fidelity and purity of the system.

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“…(3.20) of Ref. [33]). In all cases, we assume that time is much later than the inverse cut-off time.…”

Section: Appendix A: Calculational Details Of Qubit In a Thermal Bathmentioning

confidence: 99%

“…The inverse Laplace transform contains a contribution of a branch cut as well as a pole [33,34]. We ignore the contribution of the branch cut, which is negligible at all but very late times such that Γ o t > 20 and very early times such that Γ o t < 10 −21 (see Eq.…”

Section: Appendix A: Calculational Details Of Qubit In a Thermal Bathmentioning

confidence: 99%

Non-Markovian qubit dynamics in a thermal field bath: Relaxation, decoherence, and entanglement

et al. 2005

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“…[25] Replacing H ex−bosonic by H ex−P h , one can obtain the corresponding noise spectrum straightforwardly. As shown in Fig.…”

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confidence: 99%

Proposal for detection of non-Markovian decay via current noise

Chen

2008

Phys. Rev. B

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We propose to detect non-Markovian decay of an exciton qubit coupled to multi-mode bosonic reservoir via shot-noise measurements. Non-equilibrium current noise is calculated for a quantum dot embedded inside a p-i-n junction. An additional term from non-Markovian effect is obtained in the derivation of noise spectrum. As examples, two practical photonic reservoirs, photon vacuum with the inclusion of cut-off frequency and surface plasmons, are given to show that the noise may become super-Poissonian due to this non-Markovian effect. Utilizing the property of super-radiance is further suggested to enhance the noise value.PACS numbers: 03.65. Yz, 72.70.+m, 73.20.Mf, Introduction.-Due to rapid progress of quantum information science, great attention has been focused on the dynamics of systems interacting with their surroundings. Radiative decay of a two-level atom maybe one of the most obvious examples in this issue and can be traced back to such early works as that of Albert Einstein in 1917.[1] While Markovian approximation is widely adopted to treat decoherence and relaxation problems, non-Markovian dynamics of qubit systems have attracted increasing attention lately. [2] Turning to solid state systems, an exciton in a quantum dot (QD) can be viewed as a two-level system. Radiative properties of QD excitons, such as super-radiance [3] and Purcell effect [4], have attracted great attention during the past two decades. Utilizing QD excitons for quantum gate operations have also been demonstrated experimentally.[5] With the advances of fabrication technologies, it is now possible to embed QDs inside a p-i-n structure [6], such that the electron and hole can be injected separately from opposite sides. This allows one to examine the exciton dynamics in a QD via electrical currents [7].Recently, the interest in measurements of shot noise in quantum transport has risen owing to the possibility of extracting valuable information not available in conventional dc transport experiments [8]. In this work, we propose to detect non-Markovian decay of a exciton qubit via the current noise of a QD p-i-n junction. Without making Markovian approximation to the exciton-boson interaction, we analytically show that the Fano factor (zero-frequency noise) may become super-Poissonian. As examples, two practical photonic environments, photon vacuum with the inclusion of cut-off frequency and surface plasmons, are given to show this non-Markovian effect. To enhance the noise value, we further suggest utilizing the property of super-radiance.The model.-QDs can now be embedded in a p-i-n junction, such that many applications can be accomplished by electrical control. As shown in Fig. 1, we wish to see

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“…The simplest case occurs for = 0. Note that the asymptotic expansion for φ ( ) of this or a similar form is obtained for a wide class of densities of energy distribution ω( ) [14,16,17,20,21,23], [27] - [35], [39]. From the relation (51) one concludes that…”

Section: A More General Casementioning

confidence: 78%

“…19), in the case of nuclear de-excitation by γ-ray emission in order to destroy most of the exponential-decay curve, one should have to move the detector away from the source of the emission to a distance of approximately 1 6 × 10 25 [m]. Despite the negative results of the aforementioned tests, conditions leading to the nonexponential behavior of the amplitude φ ( ) at long times have been studied theoretically [27] - [33]. Conclusions from these studies were applied successfully in the experiment described in [34], where the experimental evidence of deviations from the exponential decay law at long times was reported.…”

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confidence: 99%

Long time properties of the evolution of an unstable state

Urbanowski

2009

Open Physics

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Abstract:An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. In 1957 Khalfin proved that this amplitude tends to zero as → ∞ more slowly than any exponential function of . This can be described in terms of the time-dependent decay rate γ( ) which, when considered with the Khalfin result, means that this γ( ) is not a constant for large but that it tends to zero as → ∞. We find that a similar conclusion can be drawn for a large class of models of unstable states for a quantity, which can be interpreted as the "instantaneous energy" of the unstable state. This energy should be much smaller for suitably larger values of than when is of the order of the lifetime of the considered state. Within a given model we show that the energy corrections in the long ( → ∞) and relatively short (lifetime of the state) time regions, are different. This is a purely quantum mechanical effect. It is hypothesized that there is a possibility to detect this effect by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of astrophysical and cosmological parameters.

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Deviations from exponential decay in the case of spontaneous emission from a two-level atom

Cited by 48 publications

References 8 publications

Non-Markovian qubit dynamics in a thermal field bath: Relaxation, decoherence, and entanglement

Non-Markovian qubit dynamics in a thermal field bath: Relaxation, decoherence, and entanglement

Proposal for detection of non-Markovian decay via current noise

Long time properties of the evolution of an unstable state

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