Coherence Transfer Between Atomic States By The Technique Of STIRAP And Its Applications

The thesis for doctorate consists of three parts: Coherence transfer between atomic states by the technique of STIRAP, the slow light storage transfer by STIRAP, design of quantum controlled-NOT gates by STIRAP.Coherence transfer between atomic states by the technique of STIRAPThe atomic coherence transfer process will be demonstrated in a four-level atomic (tripod) scheme by the STIRAP technique as shown in Fig.1. Fig.1 The Tripod atomic energy leverlIn Fig. 2, step-1 prepares the coherence by a fractional STIRAP process. If the pulsesω1 andω2 have the same time back edge, the atomic coherence between |1> and |2> will reach its maximum. In step-2, we apply a STIRAP process among states |2>, |3>, and |4>; the pulse sequences are shown in the right-hand side of Fig. 2(a1). By numerical simulation, we find that the component of state |2>in the state vector is fully transferred to state |3>as shown in the right-hand side of Fig. 2(a2), and the coherence between |1>and |2>is fully transferred to the coherence between |1>and |3>, as shown in Fig. 2(a3).Fig.2 Sequences of the coupling pulses, atomic state vectors and atomic coherence varies with timeBecause the states |2>and |3>are not coupled with state |4>in the STIRAP process, it does not arouse the stimulated emission from state |3> to |1>when the pulseω2 is applied. Next we will show how to control the coherence distribution by ωandω2 have the same shape functions but different amplitudes, and the ratio ofω1 andω2 is constant during the time evolution process. In step-2, the ratios of the input pulse Rabi frequencies are also constant. Ignoring the dephasing rates of the lower states, the coherence will maintain constant when the pulses vanish. Fig.3 N-levels atomic energy schemeThe above method could be expanded to an N-level system as shown in Figure 3. Every time we choose two lower levels that couple with a common exited state by two pulses, by choosing the pulse sequences and shapes we can realize the coherence transfer and contribution in a N-level system.We performed an experiment to verify the atomic coherence transfer process with 87Rb. Figure 4 shows a related level diagram of 87Rb. We choose the sublevels 5 S1 /2F= 1,m=?1, 5 S1 /2F= 2,m=?1, 5 S 1 /2F= 2,m=1 and 5 P1 /2F′=1,m=0 as the states |1>,|2>,|3>and |4>, respectively. The pulsesω1 andω2 have the same circular polarization 1 2N?1Nadjusting the intensities of three pulses. As shown in Fig.2(b), the resultscould be proved by calculation. In step-1, the back edge of input pulses σ+, and the pulseω3 has the opposite circular polarizationσ?. We detect the coherence by observing coherent Raman scattering signal; if there is coherence between the states |1> and |3>, when the read pulseω1 couples the states |1>-|4>, the coherence between |3>and |4>will be induced. From Maxwell's equations, the coherence between |3>and |4> will induce a stimulated signal, and the coherence along the direction of the signal propagation will have the same value, which will ensure that the signal is enhanced continually. Fig.4 Related energy level diagram of 87Rb.The experiment process consists of the following three steps as shown in Fig. 5: Step-0 prepares most atoms in the ground state 5 S 1 /2F=1 by an optical pumping process. Step-1 prepares the coherence. In this step, the pulse duration ofω1 is 70 ns, and that ofω2 is 160 ns. Step-2 is the coherence transfer and read process. In step-2, the pulse duration ofω2 is 30 ns, which is adjustable, and that of the pulseω3 is 60 ns, which is fixed. When the back edge of the pulseω2 crosses with the front edge of the pulseω3 and the STIRAP condition is fulfilled, the coherence between |1>and |2> is transferred to the coherence between |1>and |3>. In this step we call the pulsesω2andω3 the transfer pulses. After this process, one more pulseω1 with 40 ns duration is used as the read pulse; if the atomic coherence transfer is realized, aσ? polarized coherent Raman scattering signal will be observed. Fig.5 Pulse sequences of the fieldsThe experimental arrangement is illustrated in Fig.6. Both ECDL1 and ECDL2 are the DL-100 external-cavity diode lasers with linearly polarized output beams. Laser from ECDL1 is used asω1 , and that from ECDL2 asω2 andω3. The applied cw laser powers of these three beams passing through the cell are 6.4 mW, 3.2 mW, and 3.2 mW, respectively, and the beam diameters are about 0.1 mm. The beams pass through three acousto-optic modulators (AOMs) respectively driven by pulses with adjustable duration and delay. The P1, P2 wave plates make the beams 1 and 2 have opposite circular polarization with beam 3, and the P1 wave plate in beam 1 is movable. Atomic Rb vapor is contained in a 3.5 cm long and 2.5 cm diameter glass cell, and the temperature is about 90°C, corresponding to atomic density of 1012 cm?3. Fig.6 Experimental setup. AOM, acousto-optic modulator; L, lens; P1, P2,λ/2wave plate; P3, P4:λ/4 wave plate, PBS, polarizing beam splitter; BS, beam splitter; PD, photodiode.In the experiment, we first need create the coherence between |1>and |2>, but since the pulsesω1 andω2 have the same polarization, it cannot be separated by PBS. P1 is removed at beginning, which will make the two pulses have opposite polarization. We adjust the sequences of these two pulses to look for the maximal coherence point where the optimalσ+ signal will be observed with the read pulseω1 . When the transfer pulse is turned on, theσ+ signal will disappear as shown in Fig. 7. It means the coherence has been transferred or disappears. If P1 is put back, aσ? signal will be observed with the read pulseω1 .Changing the time delay of the transfer pulseω2 to destroy the STIRAP condition, the signal will disappear as shown in Figs. 8. Although the phenomenon is observed through two different sublevels systems, it still can prove that the coherence have been transferred. The sublevels are symmetrical; if theσ? polarizationω1 induces the coherence between 5S1/2|F=1,m=1> and 5S1/2|F=2,m=?1>, theσ+ polarizationω1 could induce the coherence between |1>and |2>.Fig.8 The relative position of the transfer pulses and the intensity of generated signal The slow light storage transfer by STIRAPIn this part we introduced a method to realize the slow light storage transfer by STIRAP. First, the slow light storage will be simulated as show in Fig.9. The states |1>,|4>,|3>are chose as storage levels, and the E1 andΩc are chose as probe field and control field. For simplicity, the dephasing rates of the three lower states are ignored. Fig.9 Relevant energy levelsA gauss shape pulse is chosen as input pulse, whose Rabi frequency is 10KHz, and the FWHM is 2.8μs as the solid line in Fig.10. the velocity of the input pulse will be slowed to 1500m/s when the Rabi frequency of the control field is 20MHz, and the FWHM of the output pulse is about 5.9μs , the Rabi frequency become 4.8KHz as the dash line in Fig.10.The input pulse and the output pulse are separated in time sequence.If the control field is switched off at some time, and the signal is still in the medium, the information will be transferred to the atomic coherence. After a period of time, the control field is switched on, the coherence will be transferred to the signal again as shown in Fig.11, and Figure 12 is the three-dimensional format of the process. The pulsesΩ1 andΩ2 are inputted as transfer pulses in the period of the switched off control field as shown in Fig.13. The two pulses must fulfilled the STIRAP condition, and it must be emphasized that the power of the pulses is more higher than common STIRAP because of the very weak atomic coherence. Fig.14 The three-dimensional scheme of the coherence transfer The atomic coherence transferred process will be clearly observed in Fig.14 when the transfer pulses are switched on. The atomic coherence between |1>and |3>decreases gradually, and it is fixed in the space, the coherence between |2>and |3>increase gradually, the coherence is transferred from |1>-|3>to |1>-|2>.The control field is switched on after the period of the transfer pulses. As shown in Fig.15, the signal field of E1 disappeared and the signal field of E 2 appeared, it is verified that the information is transferred from E1 to E 2 with the coherence transfer.The phase of the storage information could be controlled with the phase of the transfer pulses, and the transition frequency of the control field could be adjust by transfer the coherence populations of the ground state which interact with the control field.Design of quantum controlled-NOT gates by STIRAPIn 2002, Nicklas suggest that the control-NOT gates could be realized in rare-earth-ion-doped inorganic crystals. The excited state of an ion will establish a surrounding permanent dipole field, which will shift the transition frequencies of the neighboring ions and which can hence control their interaction with a laser field. For Eu in YAlO3 crystal, the excited ion could shift the transition frequencies of the neighboring ions by about 1 GHz, 1 MHz and 1 kHz for interionic distances of 1nm, 10nm and 100 nm, respectively.we can create two groups of ions i and j via an optical transition, there will be a number of i ions that are sufficiently close to some j ions so that they can control each other, the aim of the preparation is to select only these ions for the qubits. Firstly we need excite the j ions to the excited state using aπpulse. The i ions situated close enough to j ions will then shift out of their original absorption frequency because of the dipole–dipole interaction. However, i ions with no j ions close by are not affected by the j excitation and they will still absorb at their original frequency. These i ions can therefore be excluded from any further interaction by STIRAP with an aux level as shown in Fig.16. The next step is to return the j ions to the ground state by aπpulse. The result of this is that the fraction of i ions that were originally shifted out of resonance return to their original position. We now have a situation where the ions in the first frequency channel can be used as a control for the second one. Fig.16 The relevant energy levelsWe will now describe the scheme for performing a controlled-NOT operation between two qubits, i and j, where bit j is used as the control bit, and is the target bit. The j ions repared in state |0>j, when aπpulse couple the states |0>j and |exc>j, it will shift the absorption frequency of the i ions, the laser will not interact the i ions. If aπpulse couple the states |0>j and |exc>j, it will not affect the j ions or i ions, then the pulse①②③④interact with the i ions accomplishing three groups STIRAP as shown in Fig.17, if the initial state isψi =a0 0 +a11, the final state will becomeψf =a0 1 +a10. Fig.17 The relevant energy levels and the sequence of pulsesWhen the detune is small, it will not affect the STIRAP as shown in Fig.18(a). The effect of STIRAP become weak when increasing the detune. The states will not be affected by STIRAP when the detune is 1GHz. Fig.18 The peak Rabi frequency of the transfer pulses is 20MHz,Δ=2MHz, 100MHz, 500MHz, 1000MHz 141 The proposal need the big frequency shift which decided by the distance of the ions, but there is no populations appearing in the excited state in the"NOT"process, it means that the i ions will not affect other ions, so the j ions could also control other ions.