Decoherence control in different environments

We investigate two techniques for controlling decoherence, focusing on the crucial role played by the environmental spectrum. We show how environments with different spectra lead to very different dynamical behaviours. Our study clearly proves that such differences must be taken into account when designing decoherence control schemes. The two techniques we consider are reservoir engineering and quantum-Zeno control. We focus on a quantum harmonic oscillator initially prepared in a nonclassical state and derive analytically its non-Markovian dynamics in presence of different bosonic thermal environments. On the one hand we show how, by modifying the spectrum of the environment, it is possible to prolong or reduce the life of a Schr\"odinger cat state. On the other hand we study the effect of nonselective energy measurements on the degradation of quantumness of initial Fock states. In this latter case we see that the crossover between Zeno (QZE) and anti-Zeno (AZE) effects, discussed by Maniscalco et al. [Phys. Rev. Lett. 97, 130402 (2006)], is highly sensitive to the details of the spectrum. In particular, for certain types of spectra, even very small variations of the system frequency may cause a measurement-induced acceleration of decoherence rather than its inhibition.Comment: 8 pages, 4 figures, new figures added, text modified for clarit

Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.Siirretty Doriast

Role of the environmental spectrum in the decoherence and dissipation of a quantum Brownian particle

Siirretty Doriast

Finite-time quantum-to-classical transition for a Schroedinger-cat state

The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schr\"odinger cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum to classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well defined physical meaning and allow a deeper understanding of the quantum to classical transition. Our analysis shows that, for most nonclassicality measures, the Schr\"odinger cat dies after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is prerequisite for entanglement generation our results also bridge the gap between decoherence, which appears to be only asymptotic, and entanglement, which may show a sudden death. In fact, whereas the loss of coherences still remains asymptotic, we have shown that the transition from quantum to classical can indeed occur at a finite time.Comment: 9+epsilon pages, 4 figures, published version. Originally submitted as "Sudden death of the Schroedinger cat", a bit too cool for APS policy :-

Neuronavigated Versus Non-navigated Repetitive Transcranial Magnetic Stimulation for Chronic Tinnitus: A Randomized Study

Repetitive transcranial magnetic stimulation (rTMS) has shown variable effect on tinnitus. A prospective, randomized 6-month follow-up study on parallel groups was conducted to compare the effects of neuronavigated rTMS to non-navigated rTMS in chronic tinnitus. Forty patients (20 men, 20 women), mean age of 52.9 years (standard deviation [SD] = 11.7), with a mean tinnitus duration of 5.8 years (SD = 3.2) and a mean tinnitus intensity of 62.2/100 (SD = 12.8) on Visual Analog Scale (VAS 0–100) participated. Patients received 10 sessions of 1-Hz rTMS to the left temporal area overlying auditory cortex with or without neuronavigation. The main outcome measures were VAS scores for tinnitus intensity, annoyance, and distress, and Tinnitus Handicap Inventory (THI) immediately and at 1, 3, and 6 months after treatment. The mean tinnitus intensity (hierarchical linear mixed model: F3 = 7.34, p = .0006), annoyance (F3 = 4.45, p = .0093), distress (F3 = 5.04, p = .0051), and THI scores (F4 = 17.30, p F3 = 2.96, p = .0451) favoring the non-navigated rTMS. Reduction in THI scores persisted for up to 6 months in both groups. Cohen’s d for tinnitus intensity ranged between 0.33 and 0.47 in navigated rTMS and between 0.55 and 1.07 in non-navigated rTMS. The responder rates for VAS or THI ranged between 35% and 85% with no differences between groups (p = .054–1.0). In conclusion, rTMS was effective for chronic tinnitus, but the method of coil localization was not a critical factor for the treatment outcome.</p

Neuronavigated Versus Non-navigated Repetitive Transcranial Magnetic Stimulation for Chronic Tinnitus: A Randomized Study

Repetitive transcranial magnetic stimulation (rTMS) has shown variable effect on tinnitus. A prospective, randomized 6-month follow-up study on parallel groups was conducted to compare the effects of neuronavigated rTMS to non-navigated rTMS in chronic tinnitus. Forty patients (20 men, 20 women), mean age of 52.9 years (standard deviation [ SD ] = 11.7), with a mean tinnitus duration of 5.8 years ( SD  = 3.2) and a mean tinnitus intensity of 62.2/100 ( SD  = 12.8) on Visual Analog Scale (VAS 0–100) participated. Patients received 10 sessions of 1-Hz rTMS to the left temporal area overlying auditory cortex with or without neuronavigation. The main outcome measures were VAS scores for tinnitus intensity, annoyance, and distress, and Tinnitus Handicap Inventory (THI) immediately and at 1, 3, and 6 months after treatment. The mean tinnitus intensity (hierarchical linear mixed model: F 3  = 7.34, p  = .0006), annoyance ( F 3  = 4.45, p  = .0093), distress ( F 3  = 5.04, p  = .0051), and THI scores ( F 4  = 17.30, p  < .0001) decreased in both groups with non-significant differences between the groups, except for tinnitus intensity ( F 3  = 2.96, p  = .0451) favoring the non-navigated rTMS. Reduction in THI scores persisted for up to 6 months in both groups. Cohen’s d for tinnitus intensity ranged between 0.33 and 0.47 in navigated rTMS and between 0.55 and 1.07 in non-navigated rTMS. The responder rates for VAS or THI ranged between 35% and 85% with no differences between groups ( p  = .054–1.0). In conclusion, rTMS was effective for chronic tinnitus, but the method of coil localization was not a critical factor for the treatment outcome

Electric field-navigated transcranial magnetic stimulation for chronic tinnitus: a randomized, placebo-controlled study

<p><i>Objective</i>: Repetitive transcranial magnetic stimulation (rTMS) may alleviate tinnitus. We evaluated effects of electric field (E-field) navigated rTMS targeted according to tinnitus pitch. No controlled studies have investigated anatomically accurate E-field-rTMS for tinnitus. <i>Design</i>: Effects of E-field-rTMS were evaluated in a prospective randomised placebo-controlled 6-month follow-up study on parallel groups. Patients received 10 sessions of 1 Hz rTMS or placebo targeted to the left auditory cortex corresponding to tonotopic representation of tinnitus pitch. Effects were evaluated immediately after treatment and at 1, 3 and 6 months. Primary outcome measures were visual analogue scores (VAS 0–100) for tinnitus intensity, annoyance and distress, and the Tinnitus Handicap Inventory (THI). <i>Study sample:</i> Thirty-nine patients (mean age 50.3 years). <i>Results</i>: The mean tinnitus intensity (<i>F</i>₃ = 15.7, <i>p</i> < 0.0001), annoyance (<i>F</i>₃ = 8.8, <i>p</i> = 0.0002), distress (<i>F</i>₃ = 9.1, <i>p</i> = 0.0002) and THI scores (<i>F</i>₄ = 13.8, <i>p</i> < 0.0001) decreased in both groups over time with non-significant differences between the groups. After active rTMS, 42% and 37% of the patients showed excellent response at 1 and 3 months against 15% and 10% in the placebo group (<i>p</i> = 0.082 and <i>p</i> = 0.065). <i>Conclusions</i>: Despite the significant effects of rTMS on tinnitus, differences between active and placebo groups remained non-significant, due to large placebo-effect and wide inter-individual variation.</p