Effect of interactions on quantum-limited detectors

Abstract

We consider the effect of electron-electron interactions on a voltage biased quantum point contact in the tunneling regime used as a detector of a nearby qubit. We model the leads of the quantum point contact as Luttinger liquids, incorporate the effects of finite temperature and analyze the detection-induced decoherence rate and the detector efficiency, Q. We find that interactions generically reduce the induced decoherence along with the detector's efficiency, and strongly affect the relative strength of the decoherence induced by tunneling and that induced by interactions with the local density. With increasing interaction strength, the regime of quantum-limited detection (Q → 1) is shifted to increasingly lower temperatures or higher bias voltages respectively. For small to moderate interaction strengths, Q is a monotonously decreasing function of temperature as in the non-interacting case. Surprisingly, for sufficiently strong interactions we identify an intermediate temperature regime where the efficiency of the detector increases with rising temperature.

Theory of interaction-dependent instability in quantum detection by means of a Luttinger liquid tunnel junction: A rigorous theorem

“…The latter defines both decoherence time τ dec referred to the quantum state of a given charge-qubit and a "time of reaction" τ acq of the many-body quantum state of QPC on the simultaneous time-evolution of a charge-qubit quantum state; τ acq -is also widely known as the acquisition of information time. 5,6,10,41,50 These two time-scales are not the same. In reality, including the experiments of Refs.…”

“…However, interaction between measured-and detector subsystems obviously affect both, continuously changing also the quantum state of a measured subsystem being prepared initially 5,6,21,22 . In other words, interaction between measured-and detector-counterparts of any isolated quantum system leads to the gradual decoherence of both [5][6][7][8][37][38][39][40][41]50,54 . And this is the price for the most non-invasive measurements on quantum object one could ever perform by means of another (as small) quantum object (quantum detector) 9,10,50 .…”

“…Therefore, in this "effective" zerotemperature limit, both real -and measured (in the experiments of Refs. [11,12]) decoherence timescales should be referred to the only "incoherent" effect in the system which still remains relevant in this effective zerotemperature limit 5,6,10,41,50 the one is the electrostatic interaction between the electron on the DQD (i.e. chargequbit) and electrons tunneling through QPC quantum detector while latter performs a given quantum measurement on this charge-qubit.…”

“…That is why the ratio between these two timescales defines so-called quantum detector efficiency rate: Q = τ dec /τ acq ≤ 1 where the case: Q = 1 (i.e. when τ dec = τ acq and the same quantum processes of interaction are responsible both for decoherence of measured system and for its feedback to detector) is known in the literature as quantum limit of detection which is typically realized only in the absence of large thermal fluctuations in quantum system of interest 10,50 . However, as we will see below, in the case of definite weak electron-electron interactions in QPC quantum detector, even at zero-and near-zero temperatures, the acquisition of information time τ acq can be still much longer than a "true" decoherence time τ dec for a given charge-qubit interacting electrostatically with given QPC quantum detector.…”

“…Nevertheless, the properties of a described quantum detection procedure in the system: charge-qubit + tunnel junction of two 1D Luttinger liquid quantum wires have remained unclear at temperatures near the absolute zero. Physical reason for that is straightforward: at near-zero-(and zero) temperatures quantum fluctuations in Luttinger liquid tunnel junction become large with respect to thermal noise and, as the result, respective tunneling time -diverges already in its first perturbative order 39,41,[45][46][47]50,53,55 due to Kane-Fisher effect 47 . The latter means actually that an infinite number of virtual charge-qubit-assisted resonant tunnelings of interacting electrons -contributes transport characteristics of Luttinger liquid tunnel junction of interest.…”