Q uantum ballistic transport in electron waveguides (EWGs) 1,2 is based on coherent quantum states arising from the one-dimensional (1D) confinement in nanometre-scale constrictions. Semiconductor EWGs have received considerable renewed interest for quantum logic devices 3-7 and theoretical concepts [8][9][10][11] in the context of solid-state quantum information processing 12 . Implementation in real-world quantum circuits requires the unambiguous experimental distinction between all involved energy levels. However, such knowledge of EWGs investigated for wavefunction hybridization 13-15 is solely based on estimates. Here, we present coupled EWGs that allow single-mode control and manipulation of mode coupling at temperatures as high as that of liquid-helium (4.2 K) and above. We demonstrate high-resolution energy spectroscopy of each EWG subband ladder and the 1D coupled states involved. The results verify the power of advanced nanolithography and its ability to open the door to the scalable semiconductor quantum circuits envisaged today.Quantum 1D conductors formed from two-dimensional (2D) electron gases (2DEGs) are important in nanoscopic and mesoscopic semiconductor devices when studying the physics of coherent electron flow 1,2 . Spatial 1D constrictions are formed of the order of the Fermi wavelength l F ∼ 35 nm and much below the mean free path length of l ∼ 10 μm as achieved in high-electron-mobility (∼1 × 10 6 cm 2 V −1 s −1 ) 2DEGs in AlGaAs/GaAs heterostructures. Various techniques can be used, such as metal-deposited split gates 16,17 , etching 18-20 or local anodic oxidation 21 . Conductance quantization 16,17 in linear and nonlinear transport is reported for etched single EWGs for temperatures up to 30 K (ref. 19), which requires large 1D subband separations (>10 meV). So far, coupled EWGs have been restricted to 1D subband spacings of a few millielectronvolts, hampering the direct high-resolution energy spectroscopy of each single EWG and their coupled modes [13][14][15] . Only estimates of splitting energies are known 13,22 . Our objective here is to demonstrate direct high-resolution energy spectroscopy applicable to various coupled EWGs. The complete knowledge of mode-coupled 1D energy spectra is provided fulfilling a prerequisite for quantum engineering of proposed complex EWG devices 3-11 .Nanolithography with an atomic force microscope (AFM, Digital Instruments, Nanoscope III) enables us to produce EWGs showing 1D subband spacings above 10 meV allowing single-mode operation and control of mode coupling at liquid-helium temperature (4.2 K) and above.Spatially separated coupled EWGs can be realized using a tunnel barrier, either from two vertically stacked 2DEGs or from a single 2DEG with a lateral tunnel barrier. Spatially coincident coupled EWGs can also be realized, by either injecting electrons from different modes of the 2D reservoirs or by laterally merging the electron flow from two EWGs into one junction. In each case, mode coupling occurs as wavefunction hybridization 13 |Ψ +/− = a...