Quantum Telegraph Behavior Without Photons

TL;DR

This work shows that telegraph-like switching in a driven-dissipative two-level system can arise from non-Hermitian noise without invoking photon corpuscles. By combining an incoherent pumping term with a small stochastic term, the authors derive a continuous-time stochastic dynamics for the Bloch component $U_3$ that reproduces the Born-rule counting statistics and yields telegraph switching between the two qubit states. The analysis includes numerical simulations of the SDE and a Fokker-Planck treatment, revealing three dynamical regimes controlled by the noise strength parameter $ ext{alpha}$ and confirming the long-time occupancy ratio $rac{raket{t_e}}{raket{t_g}} = GT$. The results bridge weak-measurement theory, spontaneous-collapse models, and classical switching intuition, offering a photon-free interpretation of quantum jumps with potential implications for measurement and detection in quantum systems.

Abstract

We show that a simple model of non-Hermitian noise gives rise to the telegraph switching behavior seen in experiments with single qubits, without any reference to the existence of photons as corpuscles. This lends support to a continuous collapse interpretation of quantum mechanics, but can also be viewed as a model of continuous detection of a steady-state process in the incoherent limit. We show explicitly that such a system obeys the Born rule for particle counting statistics, even though no particle behavior has been invoked at any point in the calculation.

Figures (5)

• Figure 1: a) A typical "telegraph" trajectory of \ref{['eq:SDE']}, for weak continuous driving and decay. Parameter values were $dt = 10^{-4}$, $\alpha = 10$, $T = 1$, and $G = 0.6$, corresponding to $(GT-1)/(GT+1) = -0.25$. b) A typical noisy trajectory of \ref{['eq:SDE']} when the random fluctuation rate is high, for the same parameters as (1a) except $\alpha = 0.5$. c) A typical trajectory of \ref{['eq:SDE']} when the random fluctuation rate is low, for the same parameters as (1a) except $\alpha = 0.05$. In all cases the initial condition was $U_3(0) = 1$, and the data were smoothed by an instrumental resolution function with temporal width of $5\times 10^{-3}$.
• Figure 2: Ratio of time spent in the upper versus lower states as $GT$ varies, averaged over $2\times 10^8$ time steps of each simulation. Presence in one of the two states was defined as $U_3$ within 0.05 of either $+1$ or $-1$. Parameter values were $dt = 10^{-4}$, $\alpha = 10$, and $T =1$.
• Figure 3: Ratio of time spent in either the upper or lower state to the total evolution time, defined as in Figure \ref{['fig:ratio']}, averaged over $10^8$ time steps of one simulation, while varying relative strength between incoherent pumping and the random walk. Parameter values were $GT = 0.6$, $dt = 10^{-4}$, and $T =1$.
• Figure 4: a) Data for the state of a single ion under constant illumination, showing telegraph behavior. Reprinted from SauterBlattNeuhauserToschekQuantumJumps1988. b) Data for the frequency of laser emission as a function of time when there are two coupled modes. Reprinted from MorkTromborgMechanismMode1990.
• Figure 5: Probability distribution $\rho(y)$ of the system with $T = 1$, $G= 0.6$, and $t\rightarrow \infty$, computed using the Fokker-Planck equation, for four values of $\alpha$, the strength of the quantum noise term. The dashed vertical line represents the mean $(GT-1)/(GT+1)$.

Theorems & Definitions (4)

• lemma 1
• proof
• proposition 1
• proof