One of the new frontier areas of mesoscopic systems is the measurement of transport properties on the time scale comparable to or shorter than the phase coherence time of the individual electrons or the transit times of the electron through the sample.  We are currently measuring the weak localization signals at 250 mK from single 48-50 Ohm, 100 um long mesoscopic Au wires, with a width and thickness of about 100 nm.  We are using a home built reflectometer to measure both the in-phase and out-of-phase change in reflection coefficient as we sweep the magnetic field from500 Gauss.  In order to measure the phase coherence length, L_j at any frequency, we must be able to resolve changes in the reflection coefficient as small as 3x10^-6 at high frequencies and fit to the existing theory.

An example of the fractional change in the resistance of our sample as a function of magnetic field at 250 mK and a 442 MHz drive frequency is shown in Figure 1 along with the fit to theory we use to extract L_j.  The phase coherence length is 6.4 and the phase coherence time is t_j=L_j²/D=0.6ns where D is the diffusion constant of the sample.  We have reliable in-phase and out-of- phase data up to 900 MHz thus far (wt_j=4).  Above 900MHz the signal to noise deteriorates very quickly.  Figure 2 displays the frequency dependence of our data together with a fit to the expected signal for both the in-phase and out-phase components. This fit assumes no frequency dependence of any parameter including L_j and D and demonstrates that there is no additional decoherence due to frequency contrary to previous theoretical expectations that at wt_j=1 significant decoherence should occur. This is in agreement with earlier experimental work.  More recent theory suggests that only when hf/k_BT>1 should significant decoherence start to set in.  We are currently trying to work at 50 mK and frequencies as high as 10 GHz, hf/k_BT>8, in order for the first time to test this prediction. To our knowledge this frequency range has not yet been studied in any transport measurement on phase coherent mesoscopic systems but it could represent the upper limit for the frequency response of any device that relies upon electron phase coherence for operation.

Figure 1

Figure 2

Entanglement is a unique and "inexplicable" concept in quantum mechanics. It describes some sort of non-local correlation between quantum objects. Besides its importance for understanding fundamental physics, entanglement is also believed to be essential for building a quantum computer. The research in our group on entanglement is trying to demonstrate the capability of producing entangled electron spin states using solid state devices called quantum dots.

We start with a two dimensional electron gas system in a GaAs/AlGaAs heterostructure. By depositing metal gates (bright patterns in the figure below) on top of the wafer and then applying negative voltages on these gates, we are able to deplete the electrons underneath them. Therefore electrons can only move in the area where no gate is on top. By carefully designing the shape of gates, we can precisely control the motion of electrons. For example, gates 1, 2, 3, and 4 are used to form a quantum dot. The sample here shows two quantum dots placed very close to each other, only separated by the potential barrier generated by the negative voltage on gate 1. By tuning this voltage, we can vary the interaction between the electron spins, assuming the ideal case where each quantum dot houses one electron. Theory predicts that under certain conditions the two spins can form a singlet state, which is an entangled state. Thus the coupled quantum dots give us the possibility of studying entanglement in solid state devices.  

It is generally believed that only a violation of Bell's inequalities can be considered as a real demonstration of entanglement. In this particular case, it means that one should spatially separate the two spins after they interact with each other, and then perform independent single spin measurements on both electrons to investigate the correlation between their spin states. This is a formidable task with today's technology. Instead, we follow the suggestion by theorists and carry out shot noise measurements in the system. The basic idea is as follows. We inject electrons to both dots through reservoirs A and B and let them interact with each other. We then force them to come out of the dots and direct them to a beam splitter (the small opening between gates 1 and 11) where the spatial wave functions of both electrons overlap. Depending on the spin states of the electrons, they will be scattered into different out-going states. For example, in the case of two electrons in a singlet, they always go to the same direction after the beam splitter (either to reservoir C or D). This is called a bunching effect. As a result, the presence of entanglement will alter the shot noise of the currents flowing into C and D.  

We performed shot noise measurements in these samples at very low temperatures (around 70 mK). At this moment, we have some preliminary results showing a hint of entanglement. The shot noise observed has some qualitative agreements with theory. However, we are still puzzled by certain aspects of the data. In addition, a quantitative agreement is still missing.

Our work focuses on interface spin scattering in mesoscopic metallic Co-Cu-Co spin-valves showing that the spins (or intrinsic magnetic moments) of electrons can be flipped as they travel across magnetic interfaces.  We performed comprehensive measurements of the 4 probe non-local spin-injection resistance because this configuration provides an effective decoupling between spin and charge transport.  We showed that in this geometry an additional figure of merit, which characterizes the difference in the spin-flip rates for spin up and down electrons at the interface, can be measured.  We have observed a temperature-dependent asymmetry in the nonlocal resistance between parallel (R_P) and antiparallel (R_AP) relative orientations of the magnetizations in the ferromagnetic injector and detector.  Unlike the standard analysis of the spin-valve signal R_P-R_AP, which has been extensively studied, we studied in detail the symmetric contribution to resistance, R_S=(R_P+R_AP)/2 using a nonlocal geometry which eliminates any artifacts due to non-spin-related effects.  This symmetric contribution to the non-local spin injection has been previously completely overlooked and has been thought of as being an artifact.  However, our work reveals that the temperature dependent asymmetry of the nonlocal resistance carries key information about the nature of interfacial spin scattering.  We show that R_S is intrinsic to the process of spin injection and detection and signifies the presence of spin non-conserved interfaces.  At low temperatures R_S vanishes, as expected, but as temperature increases Rs increases nonlinearly, and at room temperature more than 30% of the spin transport at the detector interface between Co and Al₂O₃ involves spin-flip events.  By performing measurements over a wide temperature range it was shown that the conventional analysis of spin injection experiments is no longer valid at higher temperatures.  After carefully showing that the existence of a nonvanishing Rs is not an artifact, we find that these results can be explained by the existence of spin-dependent spin-flip scattering at the interface, which at room temperature limits the spin injection efficiency.  We believe, that in contrast to previous interpretations, the efficiency and the temperature dependence of spin injection are likely to be controlled by the spin-flip rate (a transport quantity) rather than by an estimated Curie temperature of an injector (a thermodynamic quantity). 

Future research in this area will concentrate on interfacial spin transport in magnetic tunnel junctions by means of shot noise measurements, which are extremely sensitive to the details of transport.