Hong-Ou-Mandel heat noise in the quantum Hall regime

We investigate heat current fluctuations induced by a periodic train of Lorentzian-shaped pulses, carrying an integer number of electronic charges, in a Hong-Ou-Mandel (HOM) interferometer implemented in a quantum Hall bar in the Laughlin sequence. We demonstrate that the noise in this collisional experiment cannot be reproduced in a setup with an effective single drive, in contrast to what is observed in the charge noise case. Nevertheless, the simultaneous collision of two identical levitons always leads to a total suppression even for the HOM heat noise at all filling factors, despite the presence of emergent anyonic quasiparticle excitations in the fractional regime. Interestingly, the strong correlations characterizing the fractional phase are responsible for a remarkable oscillating pattern in the HOM heat noise, which is completely absent in the integer case. These oscillations may be related to the recently predicted crystallization of levitons in the fractional quantum Hall regime.

Figure 1

Four-terminal setup for Hong-Ou-Mandel interferometry in the FQH regime. Contacts 1 and 4 are used as input terminals, while contacts 2 and 3 are the output terminals. The latter are connected to detectors where current and noise are measured.

Figure 2

HOM heat ratio ${\mathcal{R}}_Q^{\text{HOM}}$ as a function of the time delay $t_D$ for $q=1$ and temperatures $\theta =0.25\omega$ (solid lines) and $\theta =0.5\omega$ (dashed lines). The integer case (left panel) and the fractional case for $\nu =\frac{1}{3}$ (right panel) are compared. The other parameters are $W=0.1\mathcal{T}$ and $\omega =0.01{\omega }_c$.

Figure 3

HOM heat ratio ${\mathcal{R}}_Q^{\text{HOM}}$ (solid lines) and HOM charge ratio ${\mathcal{R}}_C^{\text{HOM}}$ (dashed lines) as a function of the time delay $t_D$ for $q=2$ and 4. The integer case (upper panels) and the fractional case for $\nu =\frac{1}{3}$ (lower panels) are compared. Black vertical lines demonstrate the exact correspondence of side peaks appearing in a charge and heat ratio. The other parameters are $W=0.1\mathcal{T}, \theta =0.25\omega$, and $\omega =0.01{\omega }_c$.

Figure 4

HOM heat ratio ${\mathcal{R}}_Q^{\text{HOM}}$ as a function of the time delay $t_D$ for $q=1$, 2, 3, and 4. The integer case (dashed lines) and the fractional case for $\nu =\frac{1}{3}$ (solid lines) are compared. The other parameters are $W=0.1\mathcal{T}, \theta ={10}^{-4}\omega$, and $\omega =0.01{\omega }_c$.

Figure 5

Single-drive heat ratio ${\mathcal{R}}_Q^{\text{sd}}$ (upper panel) and single-drive heat noise ${\mathcal{S}}_Q^{\text{sd}}$ rescaled with respect to $2{\mathcal{S}}_Q^{\text{sd}}-2{\mathcal{S}}_Q^{\text{vac}}$, as a function of the time delay $t_D$ for $q=1$ and temperatures $\theta =0.25\omega$ (solid lines) and $\theta =0.5\omega$ (dashed lines). The integer case (left panel) and the fractional case for $\nu =\frac{1}{3}$ (right panel) are compared. The other parameters are $W=0.1\mathcal{T}$ and $\omega =0.01{\omega }_c$. In the lower panel, green and blue horizontal solid lines correspond to the values of $\frac{{\mathcal{S}}_Q^{\text{vac}}}{2{\mathcal{S}}_Q^{\text{sd}}-2{\mathcal{S}}_Q^{\text{vac}}}$ for $\theta =0.5\omega$ at filling factors $\nu =1$ and $\frac{1}{3}$, respectively.