Quantitative analysis of electrically detected Ramsey fringes in P-doped Si

Abstract

This work describes detection of the laser preparation and subsequent coherent manipulation of the quantum states of orbital levels of donors in doped Si, by measuring the voltage drop across an irradiated Si sample. This electrical signal, which arises from thermal ionization of excited orbital states, and which is detected on a millisecond time scale by a voltmeter, leads to much more sensitive detection than can be had using optical methods, but has not before been quantitatively described from first principles. We present here a unified theory which relates the voltage drop across the sample to the wave function of the excited donors, and compare its predictions to experiments in which pairs of picosecond pulses from the Dutch free-electron laser FELIX are used to resonantly and coherently excite P donors in Si. Although the voltage drop varies on a millisecond time scale we are able to measure Ramsey oscillation of the excitation on a picosecond time scale, thus confirming that the donor wave function, and not just its excited state population, is crucial in determining the electrical signal. We are also able to extract the recombination rate coefficient to the ground state of the donor as well as the photoionization cross section of the excited state and phonon induced thermal ionization rate from the excited state. These quantities, which were previously of limited interest, are here shown to be important in the description of electrical detection, which, in our unoptimized configuration, is sensitive enough to enable us to detect the excitation of ∼10 7 donors.

Weak probe readout of coherent impurity orbital superpositions in silicon

“…We summarize the results for this work and others in Table I. In the case where the signal is proportional to either the excited-state population produced by a coherent Ramsey pair as in the previous electrical detection experiments [8,12], or to the ground-state population as in the present case of crossed-polarized probe transmission detection, τ Table I the measured time-bandwidth product deviates by 2σ or less from the expected value; i.e., it is therefore largely consistent with zero difference between observation and expectation. The agreement may be slightly improved in the two previous work cases (2 and 3 in Table I) by taking into account the convolution with the finite laser pulse.…”

“…THz-pumped orbital excitations of silicon impurities have been controlled and detected both incoherently and coherently to provide various dynamical time scales T 1 [1,8,9] (including the ionized donor recombination rate [10] and the interdonor tunneling rate [11]), T 2 [7], and T * 2 [8,12]. The Bloch sphere simply maps the population (given by the longitudinal, z component of the Bloch vector) and polarization (given by the transverse, x-y component).…”

“…T 1 describes the longitudinal relaxation, while T 2 and T * 2 describe transverse relaxation. It is typical to use incoherent readout of the incoherent decay [1,9,10] and coherent readout of the coherent decay [7,8], but it is also possible to utilize coherent readout of incoherent dynamics, as in the example of echo detection of T 1 [8], and incoherent readout of coherent dynamics, as in electrical detection of Ramsey interference [8,12]. In the latter the electrical signal arises from thermal ionization of excited orbital states, and it measures the excited state population.…”

“…Another advantage of electrical readout is that (if thermal ionization is replaced by controlled resonant tunneling through the barrier of a single electron transistor) it may be incorporated for readout of single orbital qubits in existing quantum computing schemes [13]. The disadvantage of electrical readout is that it requires very careful calibration to produce information on the fractional population difference, to confirm that the current is linear with population and to establish the proportionality constant [12]. For an optical experiment it is in principle possible to measure the fractional probe absorption relatively easily.…”

Giant multiphoton absorption for THz resonances in silicon hydrogenic donors

“…The first is that of accessing new excited states with different symmetry, e.g. the isotropic 2s rather than the axial 2p states used previously 28,38,39,40,41 . The second is that of moving from the Rydberg energies of order 10THz, difficult to reach for non-FEL sources, towards the region near a few THz, which is where certain QCL's 42 as well as mixing crystals 43 produce significant radiation.…”