Probing the intrinsic state of a one-dimensional quantum well with a photon-assisted tunneling

The photon-assisted tunneling (PAT) through a single wall carbon nanotube quantum well (QW) under influence an external electromagnetic field for probing of the Tomonaga Luttinger liquid (TLL) state is suggested. The elementary TLL excitations inside the quantum well are density ($\rho_{\pm}$) and spin ($\sigma_{\pm} $) bosons. The bosons populate the quantized energy levels $\epsilon^{\rho +}_n =\Delta n/ g$ and $\epsilon^{\rho -(\sigma \pm)}_n = \Delta n$ where $\Delta = h v_F /L $ is the interlevel spacing, $n$ is an integer number, $L$ is the tube length, $g$ is the TLL parameter. Since the electromagnetic field acts on the $\rho_{+}$ bosons only while the neutral $\rho_{-}$ and $\sigma_{\pm} $ bosons remain unaffected, the PAT spectroscopy is able of identifying the $\rho_{+}$ levels in the QW setup. The spin $\epsilon_n^{\sigma+} $ boson levels in the same QW are recognized from Zeeman splitting when applying a d.c. magnetic field $H \neq 0$ field. Basic TLL parameters are readily extracted from the differential conductivity curves.