To illustrate the new phenomena induced by the quantum observer, we consider the general and standard transport device shown in Fig. 1. Without loss of generality, this device is modeled by a simple tight-binding Hamiltonian with uniform on-site energy and nearest-neighbor hopping of 0.5 eV. For simplicity, we assume a single electron to be present in the device, though the results would not change if many electrons were active. This configuration can easily be realized experimentally in silicon heterostructures,24 with cold atoms25 or in graphene.26 Our findings are universal and apply to more general nanodevices: The geometry of the device modifies the absolute value of the current flows but not the effect itself. The nine leftmost and rightmost sites are connected to macroscopic thermal baths at different temperature. As a result, energy and particles will flow equally through the two branches. For the sake of simplicity in all this work, we set the external voltage gradient between the reservoirs to zero; all effects in heat and particle flows come from the thermal gradient and the quantum observer alone. Adding an external bias voltage would introduce another source of current but would not modify the conclusions concerning the impact of the quantum observer in the dynamics of the energy and particle flow in the nanodevice. While in this configuration energy can be exchanged via the baths, particle current is then corralled inside the device. At steady state no particle current is present, however, constant heat flows from hot to cold according to the second law of thermodynamics.

Fig. 1 Sketch of the thermo-electric transport nanodevice studied here. The nine leftmost and rightmost atoms are connected to thermal baths at temperature T H and T C , respectively. Due to this temperature imbalance, heat flows from the hot to the cold side equally through the two identical branches. This device will be used to study physical phenomena arising from local quantum observations. We tested similar devices with different geometries and lengths of the two branches. The conclusions drawn with the present configuration remain valid Full size image

While the coupling to the two thermal baths is modeled by a standard master equation,27 the quantum observer acts on one site changing the quantum coherence only as in the double-slit experiment.28 The quantum observer is assumed to be in a pure quantum state rather than in an ensemble temperature-state as thermal baths are and, therefore, cannot have a temperature associated to it. We are interested here in understanding how the particle and heat currents at steady state change when the quantum observation acts on a specific site, as indicated by the eye in Fig. 2a. For that specific case, Fig. 2b shows the heat current at steady state through the device as a function of the coupling strength to the quantum observer γ D and the amplitude of the applied thermal gradient ΔT. A positive current (red) indicates a flow from left to right. While the upper curved surface shows the energy current in the upper branch of the device, \(j_{{\rm{up}}}^h\), the flat contour-plot below corresponds to the energy flow in the lower branch, \(j_{{\rm{down}}}^h\). We emphasize that this contour plot is a projection onto the plane, hence only the color gradient indicates its strength. When the quantum observer measures the system at site labeled α, the energy current increase in the natural direction of the thermal gradient. However, even in the absence of a thermal gradient, the effect of the observation is to create a quantum heat flow from left to right. Remarkable, this local observation induces also a particle current in the upper branch from left to right, as can be clearly seen in Fig. 2c. As we are at the steady state, the corresponding particle current in the lower branch is exactly the opposite of it. As a result of the local action of the observer at site α, an unexpected particle ring-current is induced in the device that flows in clockwise direction. By symmetry, a similar measurement on site γ would give a counter-clockwise ring-current.

Fig. 2 Particle and energy currents in the steady state. In a–c, the observation is performed at site α, while in d–f on site β. b, e show the heat current in the upper, \(j_{{\rm{up}}}^h\), and lower branch, \(j_{{\rm{down}}}^h\). In order to allow comparison of the both, the upper current is plotted as a curved surface, while the lower energy current has been projected onto the plane below. We emphasize that this contour plot is a projection onto the plane, only the color gradient indicates its strength. A positive current (red) represents heat flowing from left to the right. In c, f the particle current in the upper branch is shown. A positive current indicates that a particle ring-current is flowing clockwise. The triangles labeled 1, 2, and 3 in e mark regions where the energy flow is to the right in both branches, in different directions in each branch, and to the left in both branches, respectively. A temperature gradient of 10−3 a.u. corresponds to around 300 K and a particle current of 3×10−7 a.u. orresponds to 2 nA Full size image

We now consider how this situation is modified when we change the observation site from α to β, indicated in Fig. 2d. Most surprisingly, now the heat flows change direction as seen in Fig. 2e: When no observation is performed (triangle 1), heat goes from the hot to the cold reservoirs in the upper and lower branches as expected. However, beyond a certain observer coupling strength γ D (triangle 3), the energy moves in both branches against the thermal gradient, that is, heat goes from the cold to the hot bath. Additionally, for intermediate coupling strength γ D (triangle 2) we observe energy ring-currents in counter-clockwise direction. Interestingly, the observation induces now a counter-clockwise particle ring-current, as can be seen in Fig. 2f. This is a consequence of the localization of the electronic state induced by the local observation. As the electronic density in our model is just four times larger in the leads than in the branches, the quantum observer acting on site β pulls the electron out of the right lead pushing it towards the left lead. An electronic current starts to flow in the upper branch from right to left. When instead the observation is performed close to the left lead, the particle flows in the opposite direction.

To show that this new effect is general and gives rise to even more interesting applications and quantum phenomena in more complex nanoscale systems, we next consider another device similar to the famous ‘‘Feynman’s ratchet.’’29 Quantum ratchets are transport devices driven by thermal or quantum fluctuations that have been widely studied to control the flow of particles and heat.30, 31 In order to model such a ratchet, we introduce the spatial asymmetry by changing the on-site energy levels on the parallel branches of our device shown in Fig. 3a. In the upper branch (sites α − β), the on-site energies are increased steadily by 10% as we move from left to right, which is graphically indicated by the size of the spheres. In the lower branch instead, the on-site energies increase from right to left in equal proportion. Therefore, we have created a quantum ratchet by adding two rectifiers on each branch in opposite direction. This could be experimentally realizable with techniques developed for constructing quantum ratchets in graphene,26 atom traps,32 or for molecular junctions.33 This configuration is chosen here to illustrate the differences of making a quantum observation in the top or bottom branches by breaking the top–down symmetry of the original device of Fig. 1. First, Fig. 3c shows that even without an observation a particle current flows in clockwise direction. This is because the system acts similar as a “salmon ladder” for our chosen working temperature.3 In the upper branch for instance, there is a small probability of the particle to hop from the left side each step up the ladder due to thermal fluctuations, but there is a very low probability for the particle on the right side to climb up the big drop of the ladder to then go down the ladder. Most interestingly, by adding a quantum observation on site β, the particle current decreases and later goes against the natural direction of the ratchet. When the observation is instead performed at site δ, in the bottom branch, the particle current is always in the preferred direction of the ratchet, but it can be significantly increased with stronger observation strength (See Supplemental Material). This effect can be explained by similar arguments as before for the flat geometry and is additionally illustrated as an animation in the Supplemental Material. The energy currents, as illustrated in Fig. 3b, have similar regimes as discussed before.