Pure dephasing increases partition noise in the quantum Hall effect

Abstract

Quantum Hall edge channels partition electric charge over N chiral (uni-directional) modes. Intermode scattering leads to partition noise, observed in graphene p-n junctions. While inelastic scattering suppresses this noise by averaging out fluctuations, we show that pure (quasi-elastic) dephasing may enhance the partition noise. The noise power increases by up to 50% for two modes, with a general enhancement factor of 1+1/N in the strong-dephasing limit. This counterintuitive effect is explained in the framework of monitored quantum transport, arising from the self-averaging of quantum trajectories.

Figures (6)

• Figure 1: Electronic beam splitter in graphene Wil07Aba07. A potential step separates a region where the Fermi level lies in the lower half of the Dirac cone (p-region) from a region where it lies in the upper half (n-region). Quantum Hall edge modes circulate around each region, in opposite directions (dashed and solid arrows). The edge modes are merged and mixed when they enter one end of the p-n junction, until they are again split at the other end. A voltage bias $V$ injects electrons from the source into $N_1$ modes in the p-region, a fraction ${\cal T}$ of which is transferred to the drain via $N_2$ modes in the n-region. The discreteness of the electron charge produces partition noise, modified by quantum interference effects.
• Figure 2: Monitored quantum transport model of dephasing Bee25: Phase coherent mixing of the modes (unitary operators $\hat{U}_i$) alternates with weak measurements of the occupation number of a mode (operators $\hat{P}_+,\hat{P}_-$, depending on whether the mode is found filled or empty). The string $s_i$ of ${\cal L}$ measurement outcomes selects one of the $2^{\cal L}$ quantum trajectories (here shown for ${\cal L}=3$). The corresponding Kraus operators \ref{['Krausdef']} are correlated because they contain the same set of unitary operators.
• Figure 3: Distribution of the transfer probability in the ensemble of random unitary matrices [Haar-measure distributed in ${\rm U}(N)$ with $N=2$]. The transfer probability ${\cal T}_{\bm s}$ of a single quantum trajectory is uniformly distributed in $(0,1)$, while the full transfer probability ${\cal T}$, summed over all quantum trajectories, is narrowly peaked around $1/2$. The histograms note_numerics are computed numerically from the Kraus matrix \ref{['Krausmatrixdef']}, averaged over $5000$ sets of unitaries $U_0,U_1,\ldots U_{\cal L}$, for $\varepsilon=0.5$ and ${\cal L}=10$.
• Figure 4: Noise power for the partitioning of $N$ modes into $N_1+N_2$ modes, for different values of $N_1,N_2$. The numerical results are computed from Eq. \ref{['Pnoiseformulasumps']}, for a single realization of the unitaries (no averaging), at $\varepsilon=0.8$ and ${\cal L}=10$. The analytical data points are the result \ref{['PnoiseFano']} for strong dephasing, which are a factor $1+1/N$ larger than the ensemble-averaged phase-coherent result \ref{['Pcoherent']}.
• Figure 5: Distribution of the transfer probability in the ensemble of random unitary matrices [Haar-measure distributed in ${\rm U}(N)$ with $N=2$]. The histogram is computed numerically, averaged over $10^4$ sets of unitaries $U_0,U_1,\ldots U_{\cal L}$, for $\varepsilon=0.2$ and ${\cal L}=50$. The black line is the uniform distribution \ref{['PcalTuniform']} in the small-$\varepsilon$, large-${\cal L}$ limit. This figure can be compared with Fig. \ref{['fig_ptransfer']} from the main text, for shorter ${\cal L}$ and larger $\varepsilon$, when the distribution is more rounded.