An experiment to observe Macroscopic Quantum Coherence in an rf-SQUID Xingxiang Zhou, Jonathan L. Habif, Pavel Rott, Mark F. Bocko, Marc J. Feldman Superconducting Electronics Lab, Electrical and Computer Engineering Department, University of Rochester, NY 14627
[email protected]
Abstract: We present the design of an on-chip time domain experiment to demonstrate macroscopic quantum coherence in an rf-SQUID, a superconducting loop interrupted by a Josephson junction. If successful the SQUID will serve as a qubit for a superconducting quantum computer. The chip is currently in fabrication. c 2001 Optical Society of America OCIS codes: (000.1600) Classical and quantum physics; (030.1640) Coherence
During the 1980’s the possibility of observing macroscopic quantum coherent (MQC) oscillations in an rf-SQUID, which is a superconducting loop interrupted by a Josephson junction, was predicted. This was called the “Schr¨odinger Cat experiment” [1]. As in Schr¨odinger’s gedanken experiment, a truly macroscopic object is maintained in a coherent superposition of classically distinct states until a measurement “collapses the wavefunction.” And like Schr¨odinger’s parable, a clear demonstration of rf-SQUID MQC would dramatically challenge our concepts of the quantum / classical boundary. The rf-SQUID MQC state was proposed as a candidate to serve as the qubit for a possible superconducting quantum computer [2]. Very recently, spectroscopic experiments showed the energy level structure expected for MQC phenomena in an rf-SQUID [3] and in the very similar “persistent current qubit” [4]. It is our intention to conduct a time domain experiment in which the macroscopic quantum coherent oscillations will be observed directly as they evolve.
(1) is the capacitance across the Josephson junction, is the total flux linking the rf-Squid, and is the where externally applied flux bias. The potential is given by ! " $# &%(' ,*+.) -0/ 1 ,+ ) (2) *) 32 $4 is the flux quantum. # where is the inductance of the superconducting loop and *) 2 , has two symmetrical minima, as shown in Fig. 1. The two When the rf-SQUID is biased at exactly minima correspond to two macroscopic currents flowing in opposite directions, clockwise and counterclockwise. For the the lowest two energy eigenstates are symmetrical and anti-symmetrical with respect to ) 2 parameters . So the leftwe orchoose, right well localized states are different superpositions of these two energy eigenstates. If we The Hamiltonian of the rf-SQUID system, under the assumption of no dissipation, is
prepare the rf-SQUID in one of the wells and let it evolve freely, then the probability of finding it in left or right well afterward is a sine function of the time. This is the quantum coherent oscillation that we are looking for. To observe this macroscopic quantum coherence, we must measure the flux state of the rf-SQUID after a precisely measured evolution time. We must repeat the measurement to determine the probability as a function of time. Considering these requirements the following issues must be addressed: biasing of the rf-SQUID; preparation of the initial flux localized state; timing of the measurement; readout of the flux state of the rf-SQUID; isolation from the environment to provide long enough decoherence time. Our solution to these problems is to have the whole experiment done on a superconducting chip, with all superconducting devices.
%(' #
*) 2
An equivalent circuit for the on-chip experiment is shown in Fig. 2. Some of this circuitry was first discussed in [5]. We use another rf-SQUID with large and to bias the qubit rf-Squid at . We increase the external current to the large junction until its critical current is exceeded. Then flux jumps into the loop one by one and the current
% '
Zhou et. al, An experiment to observe MQC in an rf-SQUID
ICQI/2001 Page
2
0.5
U/IcPhi0
0.4
0.3
0.2
0.1
0 −0.5
0
0.5 Flux/Phi0
$:9 ;=
#
Fig. 2. Circuit diagram for the MQC experiment. Each represents a Josephson junction. The quantum state of the rf-SQUID qubit can be measured at any increment of 100ps up to 12.8ns after the coherent evolution starts. The measurement at any given delay is repeated many times so the probabilities of being in the two potential wells can be determined as a function of time.
#
in increases. Finally we turn off the external bias current and the current in remains. This technique allows us to avoid any noise from the external bias lead. To bias the qubit rf-SQUID at a good enough precision, we have an extra fine tune line which is weakly coupled to the biasing loop and so extremely weakly coupled to the qubit SQUID itself. Our preparation of the initial state and timing of the measurement are done using circuitry derived from the RSFQ (Rapid Single Flux Quantum) logic family, which is a well established integrated digital technology utilizing picoseconds wide pulses generated by over-damped Josephson junctions [6]. A particular RSFQ cell, a DRO (destructive readout), that is inductively coupled to the biasing loop, is used to tip the potential well slightly so the system will reside in one of the two wells. A DRO is essentially a dc-SQUID with two stable states, one with a steady current flowing in its inductor loop (“1” state) and the other one with no current flowing (“0” state). The DRO is first in the “1” state and the system is prepared in one of the two wells. An initial pulse starts a 10GHZ clock and also resets the DRO to the “0” state, so the potential becomes symmetrical and the qubit SQUID begins to evolve freely. After a programmed delay, the clock signal is fed to the measuring apparatus and the state of the qubit SQUID is measured. Our measuring apparatus is described here for the first time. An earlier design [5] employed a high-current SFQ comparator embedded in the qubit SQUID. We have now replaced this with the design shown in Fig. 2. This is inspired by the quasi-one-junction SQUID (QOS) used for high sensitivity Josephson analog-to-digital converters. The QOS circuit at the bottom right of the figure is inductively coupled to the qubit. The timing circuits at the top of the figure provide a sampling SFQ pulse to the QOS, which is calibrated to give an output iff the qubit SQUID current is clockwise. The QOS is only sensitive to the state of the qubit current during the picosecond sampling time. A further redesign for the measuring apparatus is under evaluation. In every case, the qubit Josephson junction critical
Zhou et. al, An experiment to observe MQC in an rf-SQUID
ICQI/2001 Page
%0?
3
%0? %0?
current must be adjustable so that precisely the desired value can be attained during the experiment. To do this is chosen larger than the target value and a magnetic field generated by a control current is used to decrease down to the target value. We can use this as part of a read-out scheme if the control current can be abruptly switched off (this can be done using a DRO cell as described above). Then abruptly increases, within a few picoseconds, essentially instantaneous on the time scale of the qubit evolution. The height of the barrier in the middle of the rf-SQUID doublewell potential increases with , and the system is forced to choose to stay in one of the two wells, as if frozen. In this way the wave function of the qubit SQUID is “collapsed” at the given moment. Then the state of the rf-SQUID can be measured classically, at leisure, using techniques such as a weakly coupled dc-SQUID, copied from others’ experiments. This process is repeated many times and the probabilities of being in the two wells can be measured as a function of time. If a sinusoidal dependence is discovered, then the macroscopic quantum coherence in the rf-SQUID is proved.
%0?
%@?
The key to the success of this experiment is that the qubit has to be isolated very well from the environment so the decoherence time is long enough. (A nanosecond coherence time would allow ten ticks of our 10 GHz clock.) Our all-superconducting realization proves to help greatly. The superconducting energy gap allows that there will be no low-lying excitations at low temperature, if sufficient care is taken. The active part, the RSFQ circuits, are not coupled to the qubit except during read-out. This is because Josephson junctions are highly nonlinear and act essentially like a short circuit for small disturbances which would contribute to decoherence. We do not have any off-chip leads which are directly coupled to the qubit. Also, great care has been taken to make sure the real impedance seen by the qubit is very large. The MQC experimental chip described here (the version shown in Fig. 2.) is currently in fabrication at the MIT Lincoln Laboratories. This is our first attempt to perform this experiment. The fabrication requirements are quite rigorous, in ) Nb/Al Josephson junctions with very high quality on a chip with that the experiment calls for several small (0.5 about 100 larger junctions. A preliminary version of this experiment, using Josephson junctions much too large for MQC, was fabricated and tested as early as 1998.
A=B
Research supported in part by ARO grant DAAG55-98-1-0367. References 1. A. J. Leggett, “Schr¨odinger’s Cat and her Laboratory Cousins”, Contemp. Phys. 25, 583-98 (1984). 2. M. F. Bocko, A. M. Herr, M. J. Feldman, “Prospects for Quantum Coherent Computation Using Superconducting Electronics”, IEEE Tran. Appl. Supercond. 7, 3638-41 (1997). 3. J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, J. E. Lukens, “Quantum Superposition of Distinct Macroscopic States”, Nature 406, 43-45 (2000). 4. Caspar. H. van de Wal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M Harmans, T. P. Orlando, S. Lloyd, J. E. Mooij, “Quantum Superposition of Macroscopic Persistent-Current States”, Science 290, 773-7 (2000). 5. M.J. Feldman and M.F. Bocko, “A Realistic Experiment to Demonstrate Macroscopic Quantum Coherence”, Physica C 350, 171-6 (2001). 6. K. K. Likharev, V. K. Semenov, “RSFQ Logic/Memory Family: a New Josephson-Junction Technology for Sub-Terahertz-Clock-Frequency Digital Systems,” IEEE Tran. Appl. Supercond. 1, 3-28 (1991).
