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SUMMARY:Occupation-conservation transition in a quantum two-level system
DTSTART;VALUE=DATE-TIME:20201221T144000Z
DTEND;VALUE=DATE-TIME:20201221T150000Z
DTSTAMP;VALUE=DATE-TIME:20260419T012824Z
UID:indico-contribution-190@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Oleh Ivakhnenko (B. Verkin ILTPE of NASU)\nWhen we d
 rive quantum two-level systems (or qubits) by periodical signals\, we obta
 in repeatedly Landau-Zener-Stückelberg-Majorana (LZSM) transitions\, whic
 h relates to the tunneling in qubits [1]. Recent interest for studying the
 se repeated transitions is caused by the success in creation of the first 
 quantum computing machines which are based on different types of connected
  driven qubits. We describe a transfer matrix (TM) approach [2]\, and its 
 area of usability\, for a single LZSM transition which started from a supe
 rpositional state. As the result\, we obtain a formula for describing the 
 final occupation probability with any superpositional initial state. We co
 nsider three types of a single transition\, with: 1. Constructive interfer
 ence\, 2. Destructive interference\, and 3. Occupation-conservation transi
 tion. The last one allows us to save the same occupation probability as be
 fore the transition. TM can also be used for describing repetitive transit
 ions by using the result of the current transition as the initial conditio
 n for the next one. Previously in Ref. [3] the "transitionless transitions
 " in qubits were studied\, there the author described only the case when i
 nitially a qubit was not in any superpositional state\, but rather only in
  one of the basis states.  In Fig. 1 we demonstrate constructive and destr
 uctive transition in comparison with numerical and analytic solution on th
 e left side and occupation conservation case in the right panel\, where al
 so we demonstrated the range of possible final occupation probabilities.\n
 \nFig. 1. (left) Constructive and destructive LZSM transitions\, (right) O
 ccupation-conservation transition\, where the probability after passing th
 e avoided-level crossing is exactly the same as it was initially. Both pan
 els are plotted with the same initial conditions $P_{+i}=0.2$\, the same p
 arameters defining the transition probability\, if starting from the groun
 d state\, $P_{LZSM}=0.081$\, and with the initial phase difference $\\phi_
 i$ being different in each case.\n\nAcknowledgment:\nResearch of O.V.I. an
 d S.N.S. is sponsored by the Army Research Office and is accomplished unde
 r Grant Number W911NF-20-1-0261.\n\n[1] O.V. Ivakhnenko\, S.N. Shevchenko\
 , and F. Nori «Landau-Zener-Stückelberg-Majorana (LZSM) transitions for 
 interferometry and quantum control»\, in preparation.\n[2] B. Damski and 
 W. H. Zurek\, «Adiabatic-impulse approximation for avoided level crossing
 s: from phase-transition dynamics to Landau-Zener evolutions and back agai
 n»\, Phys. Rev. A 73\, 063405 (2006).\n[3] M. V. Berry\, «Transitionless
  quantum driving»\, J. Phys. A: Math. Theor. 42\, 365303 (2009).\n\nhttps
 ://indico.bitp.kiev.ua/event/7/contributions/190/
LOCATION:Online meeting
URL:https://indico.bitp.kiev.ua/event/7/contributions/190/
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